Integrated mid-infrared, far infrared and terahertz optical Hall effect (OHE) instrument, and method of use

ABSTRACT

System Stage, and Optical Hall Effect (OHE) system method for evaluating such as free charge carrier effective mass, concentration, mobility and free charge carrier type in a sample utilizing a permanent magnet at room temperature.

This Application Claims benefit of Provisional Application No.62/070,239 filed Aug. 18, 2014.

SUPPORT

The invention claimed herein was supported in part under Army ResearchOffice (D. Woolard, Contract No. W911NF-09-C-0097) and NSF Grant Nos.MRSEC DMR-0820521 DMR-0907475, EPS-1004094 with primary support underMRI DMR-0922937. Additional support was provided by the University ofNebraska, the J.A. Woollam Co. and the J.A. Woollam Foundation. TheUnited States Government might have certain rights in the invention.

TECHNICAL AREA

The present invention relates to Hall Effect measurement systems, andmore particularly to an integrated visual, mid-infrared, far-infraredand terahertz Optical Hall Effect (OHR) instrument, covering anultra-wide spectral range from 3 cm⁻¹ to 7000 cm⁻¹ (0.1-210 THz or0.4-870 meV), and methodology of its use in determining such as freecharge carrier longitudinal and transverse effective masses,concentration, mobility and charge carrier type. One embodimentcomprises sub-systems, including a magneto-cryostat-transfer sub-systemthat enables the usage of a magneto-cryostat sub-system with a visible,mid-infrared ellipsometer sub-system, and a far-infrared/terahertzellipsometer sub-system. An electromagnetic beam (EM) providing Sourcesub-system can be applied to provide a variable angle-of-incidence, to asample, in spectroscopic ellipsometers in reflection or transmissionmode, and comprises, in a desired wavelength range, at least one lightsource and detector. The ellipsometer sub-systems can be operated inrotatable polarizer-sample-rotating-analyzer configuration grantingaccess to the upper left 3×3 block of the normalized 4×4 Mueller matrix.The closed cycle magneto-cryostat sub-system provides sampletemperatures between room temperature and 1.4 degrees K, and magneticfields up to 8 T, enabling the detection of transverse and longitudinalmagnetic field-induced birefringence, which can be enhanced by aresonance cavity effect. A preferred embodiment, which is focal in thepresent invention, replaces the magneto cryostat with a smaller (0.8-1.6T) permanent magnet, and results produced therewith are easier to obtainand apply, especially in less substantial lab settings.

BACKGROUND

The Optical Hall Effect (OHE) is a physical phenomenon which describesthe occurrence of transverse and longitudinal magnetic field-inducedbirefringence, caused by the nonreciprocal magneto-optic response ofelectric charge carriers. The term (OHE) is used since the classicelectrical Hall Effect (HE), and the (OHE) effect both find explanationwithin the Drude model. The term Optical Hall Effect (OHE) is used inanalogy to the classic electrical Hall Effect as the electrical Halleffect and certain cases of (OHE) observation can be explained byextensions of the classic Drude model for the transport of electrons inmatter, (eg. Metals). For the (OHE), Drude's classic model is extendedby a magnetic field and frequency dependency, describing the electron'smomentum under the influence of the Lorentz force. As a result ananti-symmetric contribution is added to the dielectric tensor, the signof which depends on the type of the free charge carrier (electron orhole). The non-vanishing off-diagonal elements of the dielectric tensorreflect the magneto-optic birefringence, which lead to conversion of[p]-polarized into [s]-polarized electromagnetic waves, and vice versa.The (OHE) allows determination of concentration, mobility, and effectivemass of the free electrons as the (OHE) can be quantified in terms ofthe Mueller matrix, which characterizes the transformation of anelectromagnetic wave's polarization state. Experimentally the Muellermatrix is measured by Generalized Ellipsometry (GE), which allows foradjustment of the Angle and the Plane of Incidence a beam ofelectromagnetic radiation makes with respect to a sample surface, aswell as rotation of a sample about a perpendicular to said samplesurface. Further, during a (GE) measurement different polarizationstates of the incident light are prepared and their change uponreflection from or transmission through a sample is determined.

Optical Hall Effect (OHE) instruments conduct GE measurements on samplesin high quasi-static magnetic fields, and detect the magnetic fieldinduced changes of the Mueller matrix. Though several instruments withpartial (OHE) capability are described in the literature, most thereofdo not fulfill all desirable criteria for a true (OHE) instrument. Forinstance, in 1985 Nederpel and Martens, published an article, (seeReview of Scientific Instruments, 56,687 (1985)), reported developmentof a single wavelength (444 nm) magneto-optical ellipsometer for use inthe visible spectral range, but the instrument provided only lowmagnetic fields, (ie. B less than 50 mT). An instrument providing highermagnetic fields with spectroscopic generalized ellipsometry capabilitiesin the visible spectral range and a vector magnet, (ie. B in the rangeof 0.4 T) was presented in 2003 by Cerne et al., (see Review ofScientific Instruments, 74, 4755 (2003)). This article presented amagneto-polarimetry instrument which provided a higher magnetic fieldstrength, (ie. B up to 8 T), for use in the mid-infrared spectral range,(ie. spectral lines of a CO₂ laser), and in 2004 Padilla et al.developed a terahertz-visible, (ie. 6 to 20000 cm⁻¹ wavelength),magneto-reflectance and transmittance instrument, (ie. a B less than orequal to 9 T), (see Review of Scientific Instruments, 74, 4710, (2004)).While both instruments provide high magnetic fields, and containpolarizers and photo-elastic-modulators, these instruments were notdesigned to record Mueller matrix data (GE).

A THz time-domain spectroscopy based instrument capable of recording thecomplex reflection coefficients at magnetic B fields of about 0.5 T wasdescribed in 2004 by Ino et al., (see Phys. Rev. B 70, 155101, (2004)).A full 4×4 Mueller matrix in the terahertz-mid-infrared spectral range(20 to 4000 cm⁻¹) can be measured by an instrument described in 2013 byStanislavchuk et al., (see Review of Scientific Instruments, 84, 023901,(2013)), but there the instrument was not designed for experiments withthe sample exposed to external magnetic fields.

The first full (OHE) instrument was developed and demonstrated in 2006by Inventor herein, Hofmann, (see Review of Scientific Instruments, 77,63902, (2006)) for the far-infrared (FIR) spectral range (30 to 650cm⁻¹), which provided magnetic fields up to 6 T and allowed sampletemperatures between 4.2 K and room temperature. This first fullcapability (OHE) instrument has since been successfully used todetermine free charge carrier properties including effective massparameters for a variety of material systems. Later, (OHE) experimentswere conducted in the terahertz (THz) spectral range, but were limitedto room temperature and low magnetic fields (ie. B fields less than orequal to 1.8 T), and are subject of the invention disclosed herein.

Since the magnitude of the (OHE) depends on the magnetic field strength,higher magnetic fields facilitate the detection of the OHE. Furthermore,the sensitivity to the (OHE) is greatly enhanced by phonon modecoupling, surface guided waves and Fabry-Perot interferences. Sincethese effects appear from the THz to the mid-infrared (MIR) spectralrange, depending on the structure and material of the sample, it canbecome necessary to extend the spectral range covered by (OHE)instrumentation. An (OHE) instrument for the MIR, for example, candetect the magneto-optic response of free charge carriers enhanced byphonon modes present in the spectral range above 600 cm⁻¹, which appliesto many substrate materials, SiC, Al₂O₃ or GaN, as well as to manymaterials used for thin films, III-V nitride semiconductorsAl_(1-x)Ga_(x)N In_(1-x)N Al_(1-x)In_(x)N or In_(1-x)Ga_(x)N. Inaddition, inter-Landau-level transitions can be studied in the MIRspectral range with a MIR (OHE) instrument. The extension to the THzspectral range enables the detection of the (OHE) in samples with lowcarrier concentrations. Furthermore, the strongest magneto-opticresponse can be observed at the cyclotron resonance frequency, whichtypically lies in the microwave/THz spectral range for moderate magneticfields, (eg. a few Tesla), and effective mass values comparable to thefree electron mass.

With the foregoing insight it is noted that the present inventionpresents an (OHE) instrument that covers an ultra-wide spectral rangefrom 3/cm to 7000/cm, (ie. 0.1-210 THz or 0.4-870 meV), which combinesMIR, FIR and THz magneto-optic generalized ellipsometry in a singleinstrument. This integrated MIR, FIR and THz (OHE) instrument canincorporate a commercially available, closed cycle refrigerated,superconducting 8 Tesla magneto-cryostat sub-system, with four opticalports, providing sample temperatures between T=1.4 K and roomtemperature. However, the preferred embodiment applies at least onepermanent magnet with strength in the range of 0.6 to 1.8 T. Theellipsometer sub-systems used to actually achieve results reportedherein, were built in-house and operate in the rotating-analyzerconfiguration, (a non-limiting election), and are capable of determiningthe normalized upper 3×3 block of the sample Mueller matrix. Said (OHE)provides insight into free charge carrier properties such as effectivemass (m), mobility (u), and carrier concentration (N) of complex andeven layered samples. It is noted that the optical Hall Effect (OHE)reveals fundamental symmetry properties of the magneto-optic dielectrictensor.

For insight it is noted that operation of the integrated MIR, FIR andTHz (OHE) instrument described was demonstrated by three sample systems.Combined experimental data from the MIR, FIR and THz spectral range of asingle epitaxial graphene sample, grown on a 6H—SiC substrate by thermaldecomposition were achieved. The MIR (OHE) data of the same epitaxialgraphene sample was investigated to demonstrate the operation of the MIRellipsometer sub-system of the integrated MIR, FIR and THz (OHE)instrument, over the full available magnetic field range of theinstrument. The magneto-optic response of free charge carriers andquantum mechanical inter-Landau-level transitions were observed, andtheir polarization selection rules obtained therefrom noted. A Te-doped,n-type GaAs substrate served as a model system for the FIR spectralrange of the FIR/THz ellipsometer sub-system. The (OHE) signaloriginating from valence band electrons in a bulk material were noted,and the concentration, mobility, and effective mass parameters of thevalence band electrons determined. Finally, (OHE) data from an AlGaN/GaNhigh electron mobility transistor structure (HEMT) from the THz spectralrange of the FIR/THz ellipsometer sub-system were achieved and analyzed.The data was recorded at different temperature between T=1.5 K and roomtemperature, representing the full sample temperature range of theinstrument. The results achieved at room temperature were especiallyimportant as regards the present invention.

In this Background Section, in what directly follows, dielectric andmagneto-optic dielectric tensors are described, a brief theoreticaloverview on Mueller matrices and GE data-acquisition is given, andgeneral GE data analysis procedures are introduced. In the DetailedDescription and Drawing Sections of this Application a description of arelevant, but not-necessarily limiting experimental setup is described,along with data acquisition and data analysis procedures for (OHE) data,and examples of experimental results demonstrating the operation of theintegrated MIR, FIR and THz (OHE) instrument are presented anddiscussed.

Continuing, the evaluation of physically relevant parameters from the(OHE) requires the experimental observation and quantification of theOHE, and a physical model to analyze (OHE) data. Experimentally, the(OHE) is quantified in terms of the Mueller matrix M_(OHE) by employingGeneralized Ellipsometry (GE). The physical model which is used toanalyze the observed transverse and longitudinal magneto-opticbirefringence of the (OHE) is based on the magneto-optic dielectrictensor ∈_(oeh) (B), which is a function of the slowly varying externalmagnetic field B. If, among other parameters, the magneto-opticdielectric tensor of a sample is known, experimental Mueller matricesM_(OHE) can be modeled from ∈_(oeh) (B) using the relationship:M _(OHE)(∈_(oeh)(B)).Although this equation is in general not invertible analytically, it canbe used to determine the magneto-optic dielectric tensor fromexperimental Mueller matrix data through non-linear model mathematicalregression analysis. Dielectric tensors, Mueller matrix calculus,generalized ellipsometry including data acquisition, as well as dataanalysis are further addressed in this section.Magneto-Optical Dielectric Tensors

The optical response of a sample is here described by the dielectrictensor C. If the dielectric tensor of the sample without a magneticfield is given by ∈_(B=0) and the change of the dielectric tensorinduced by a magnetic field B is given by ∈_(B), the dielectric tensordescribing the (OHE), can be expressed as:∈_((OHE))=∈_(B=0+)∈_(B).The magneto-optic permittivity of a material within a given sampledescribed by ∈_(B) may originate from the response of bound and unboundcharge carriers subjected to the magnetic field and the action of theLorentz force. The magneto-optic response of a sample subjected to theintegrated MIR, FIR and THz (OHE) instrument, and which is addressedherein is represented by a generally anisotropic and nonreciprocaltensor. Thus, the corresponding magneto-optic contributions X₊ and X⁻ tothe permittivity tensor χ=∈−I, (where I is the 3×3 identity matrix),originate from the interaction of right- and left-handed circularlypolarized light with the sample, respectively. Without loss ofgenerality, if the magnetic field B is pointing in vector directionindicated by P=∈₀χE, it can be described by arranging the electricfields in their circularly polarized eigensystem E_(e)=(E_(x)+iE_(y),E_(x)−iE_(y), E_(z))=(E₊, E⁻, E_(z)) byP_(e)=∈₀×_(e)E_(e)=∈₀(χ₊E₊,χ⁻E⁻,0), where i=sqrt{−1} is the imaginaryunit. Transforming P_(e) back into the laboratory system the change ofthe dielectric tensor induced by the magnetic field takes the form:

$\begin{matrix}{ɛ_{n} = {\frac{1}{2}\begin{pmatrix}\left( {{{X++}X} -} \right) & {i\left( {X + {- X} -} \right)} & 0 \\{- {i\left( {{{X++}X} -} \right.}} & {{{X++}X} -} & 0 \\0 & 0 & 0\end{pmatrix}}} & (3)\end{matrix}$Note, under field inversion B is reversed into −B, the polarizabilitiesfor left- and right-handed circularly polarized light interchange. ∈_(B)is only diagonal if χ₊=χ⁻, and otherwise non-diagonal withanti-symmetric off diagonal elements.Classic Dielectric Tensors (Lorentz-Drude Model)

Charges carriers, subject to a slowly varying magnetic field obey theclassical Newtonian equation of motion (Lorentz-Drude model):m{umlaut over (x)}+mγ{dot over (x)}+mω ₀ ² x=qE+q({umlaut over(x)}×B),  (4)where: m, q, μ=qm⁻¹γ⁻¹, x and ω_(D) represent the effective mass tensor,the electric charge, the mobility tensor, the spatial coordinate of thecharge carrier and the Eigen-frequency of the un-damped system withoutexternal excitation and magnetic field, respectively. For a timeharmonic electromagnetic plane wave with an electric field E→E exp(−iωt)with angular frequency ω, the time derivative of the spatialdisplacement of the charge carrier is {dot over (x)}=v exp(iωt), where vis the velocity of the charge carrier. With j=nqv Eq. 4 reads:

$\begin{matrix}{{E = {\frac{1}{nq}\left\lbrack {{i\;\frac{m}{q\;\omega}\left( {{\omega_{0}^{2}I} - {\omega^{2}I} - {i\;{\omega\gamma}}} \right)j} + \left( {B \times j} \right)} \right\rbrack}},} & (5)\end{matrix}$where n is the charge carrier density. With the Levi-Cevita-Symbol∈_(ijk), (note, in the following-equation the Einstein notation is used,and the covariance tensor and contravariance is ignored since allcoordinate systems are Cartesian, and the summation is only executedover pairs of lower indices), the conductivity tensor σ, the dielectricconstant ∈₀, and using E=σ^(−i)j and

$ɛ = {\frac{1}{l\; ɛ_{0}\omega}\sigma}$the dielectric tensor for charge carriers subject to the externalmagnetic field B can be expressed as:

$\begin{matrix}{ɛ_{ik} = {{\frac{{nq}^{2}}{ɛ_{0}}\left\lbrack {{m_{ik}\left( {\omega_{0}^{2} - \omega^{2} - {i\;{\omega\gamma}_{ik}}} \right)} - {i\;{\omega\varepsilon}_{ijk}{qB}_{j}}} \right\rbrack}^{- 1}.}} & (6)\end{matrix}$Polar Lattice Vibrations, (Lorentz Oscillator)

For isotropic effective mass tensors the cyclotron frequency can bedefined, and for the mass of the vibrating atoms of polar latticevibrations, the cyclotron frequency is several orders of magnitudesmaller than for effective electron masses, and can be neglected for themagnetic fields and spectral ranges discussed in this paper. Therefore,the dielectric tensor of polar lattice vibrations ∈^(L) can beapproximated using Eq. 6 with B=0. When assuming isotropic effectivemass and mobility tensors, the result is a simple harmonic oscillatorfunction with Lorentzian-type broadening. For materials withorthorhombic symmetry and multiple optical excitable lattice vibrations,the dielectric tensor can be diagonalized to:

$\begin{matrix}{ɛ^{L} = \begin{pmatrix}\left( {ɛ\frac{L}{X}} \right) & 0 & 0 \\0 & {ɛ\frac{L}{Z}} & 0 \\0 & 0 & {ɛ\frac{L}{Z}}\end{pmatrix}} & (7)\end{matrix}$Where ∈^(l)/_(k) for (k=(x,y,z,)) is given by:

${ɛ\frac{L}{K}} = {ɛ_{\infty,K}{\prod\limits_{j = 1}^{i}\;\frac{{{\omega\; 2} + {i\;{\omega\gamma}\; L\; 0}},{{k\; j} - {\omega 2}_{{L\; 0},{kj}}}}{{{\omega\; 2} + {i\;{\omega\gamma}\; T\; 0}},{{k\; j} - {\omega 2}_{{T\; 0},{kj}}}}}}$Where ω_(LO,kj), γ_(LO,kj), ω_(TO,kj), and γ_(TO,kj) denote the k(x,y,z)component of the frequency and the broadening values of the j^(th)longitudinal optical (LO) and transverse optical (TO) phonon modes,respectively, while the index j runs over l modes. Further details canbe found in Hofmann et al., Applied Physical Letters 88, 042105 (2006);Barker, Phys. Rev., 136, A1290 (1964); Berryman et al. Phys. Rev. 174,791, (1968); Gervais et al., J. Phys. C 7, 2374, (1974); Hofmann et al.,Phys. Rev. B, 66, 19504 1 (2002)1 and a discussion of the requirementsto broadening parameters, such as Im(∈^(L)/_(K)) greater than or equalto 0.0 are found in Kasic et al., Phys. Rev. B 61,7365, (2000).Free Charges Carriers (Extended Drude Model)

For free charge carriers no restoring force is present and theEigen-frequency of the system is ω₀=0. For isotropic effective mass andconductivity tensors, and magnetic fields aligned along the z-axis Eq. 6can be written in the form for B=0.

$\begin{matrix}{{ɛ_{B = 0}^{D} = {{{- \frac{\omega_{P}^{2}}{\omega\left( {\omega + {i\;\gamma}} \right)}}I} = {ɛ^{D}I}}},} & (9)\end{matrix}$where

$\omega_{P} = \sqrt{\frac{{nq}^{2}}{m\; ɛ_{0}}}$is the plasma frequency, and ∈^(D) is permittivity function of theisotropic Drude dielectric function. The magneto-optic contribution tothe dielectric tensor ∈_(B) ^(D) for isotropic effective masses andconductivities can be expressed, using Eq. 3, through polarizabilityfunctions for right- and left-handed circularly polarized light:

$\begin{matrix}{{\chi_{\pm} = {- \frac{ɛ^{D}}{1 \mp \frac{\omega + {i\;\gamma}}{\omega_{c}}}}},} & (10)\end{matrix}$where

$w_{c} = \frac{q{B}}{Tn}$is the isotropic cyclotron frequency.Non-Classic Dielectric Tensors (Inter-Landau-Level Transitions)The permittivity tensor ∈_(B) ^(LL) describing the contribution of aseries of inter-Landau-level transitions to the dielectric tensor can beapproximated by a sum of Lorentz oscillators. The quantities χ± in Eq.(3) are then expressed by:

$\begin{matrix}{{\chi_{\pm} = {e^{{\pm \; i}\;\phi}{\sum\limits_{k}\frac{A_{k}}{\omega^{2} - \omega_{0,k}^{2} - {i\;\gamma_{k}\omega}}}}},} & (11)\end{matrix}$where A_(k), ω_(0,k), and γ_(k) are amplitude, transition energy, andbroadening parameter of the k^(th) inter Landau-level transition,respectively, which in general depend on the magnetic field. The phasefactor was introduced here to describe the experimentally observed lineshapes of all Mueller matrix elements.

For inter-Landau-level transitions in graphite or bi-layer graphene wefind φ=π/4, and for inter-Landau-level transitions in single layergraphene φ=0.

Note that for φ=0, the polarizabilities for left and right handedcircularly polarized light are equal, (χ₊=χ⁻), and ∈_(B) ^(LL) isdiagonal.

Mueller Matrix Calculus, GE and Data Acquisition

Generalized ellipsometry (GE) extends standard, isotropic ellipsometry(SE) to arbitrary anisotropic and depolarizing samples by includingrotation about a perpendicular to a sample surface, and can reveal thecomplex 3×3 dielectric tensor of the material investigated. This sectiondescribes the Jones vector/Mueller matrix formalism used in GE, aspectsof Mueller matrix and (OHE) data, and the acquisition of Mueller matrixdata.

Stokes Vector/Mueller Matrix Calculus

The real-valued Stokes vector S has four components, carries thedimensions of intensity, and can quantify any polarization state ofplane electromagnetic waves. If expressed in terms of the p- ands-coordinate system Stokes vector S has four components, carries theunits of intensity, and can quantify any polarization state of planeelectromagnetic waves. Expressed in terms of p- and s-coordinates, itsindividual terms can be defined as S₁=I_(p)+I_(s), S₂=I_(p)−I_(s);S₃=I₄₅−I⁻⁴⁵, and S₇=I_(σ+)−I_(σ−), with I_(p), I_(s), I₄₅, I_(σ+), andI_(σ−) being intensities for the p-. s-+45°, −45°, right and left handedcircularly polarized light components, respectively. (See R. M. Azzamand N. M. Bashara, “Ellipsometry and Polarized Light”, North-HollandPubl. Co., Amsterdam, (1984)).

The real-valued 4×4 Mueller matrix M describes the change ofelectromagnetic plane wave properties (intensity, polarization state),expressed by a Stokes vector S, upon change of the coordinate system orthe interaction with a sample, optical element, or any other matter:

$\begin{matrix}{{S_{i}^{({out})} = {\sum\limits_{i = 1}^{3}{Mijs}_{i}^{({in})}}},\left( {j = {1\mspace{14mu}\ldots\mspace{14mu} 4}} \right),} & (12)\end{matrix}$Where S^((out)) and S^((in)) denote the Stokes vectors of theelectromagnetic plane wave before and after the change of the coordinatesystem, or an interaction with a sample, respectively. Note that allMueller matrix elements of the GE data discussed in this paper, arenormalized by the element M₁₁, therefore M_(ij) is less than or equal toand M₁₁=1.Mueller Matrix and (OHE) Data

The Mueller matrix can be decomposed in 4 sub-matrices, where the matrixelements of the two off-diagonal-blocks:

$\begin{bmatrix}{M\; 13} & {M\; 14} \\{M\; 23} & {M\; 24}\end{bmatrix} = \begin{bmatrix}{M\; 21} & {M\; 14} \\{M\; 41} & {M\; 42}\end{bmatrix}$only deviate from zero if p- to s-polarization mode conversion appears,while the matrix elements in the two on-diagonal-blocks:

$\begin{bmatrix}{M\; 13} & {M\; 14} \\{M\; 23} & {M\; 24}\end{bmatrix} = \begin{bmatrix}{M\; 21} & {M\; 14} \\{M\; 41} & {M\; 42}\end{bmatrix}$mainly contain information about p- to s-polarization mode conversion,while the matrix elements in the two on-diagonal-blocks mainly containinformation about p-s-polarization mode conserving processes. It is tobe appreciated that p- to p-polarization mode conversion is defined asthe transfer of energy from the p-polarized channel of anelectromagnetic plane wave to the s-polarized channel, or vice versa.Polarization mode conversion can appear when the p-s-coordinate systemis different for S^(in) and S^(out), or, when a sample showsbirefringence, for example. In particular, polarization mode conversionappears if the dielectric tensor of a sample possesses non-vanishingoff-diagonal elements. Therefore, in Mueller matrix data from opticallyisotropic samples, ideally all off-diagonal-block elements vanish,while, for example, magneto-optic birefringence can cause non-zerooff-diagonal-block elements in the Mueller matrix.Here, we define (OHE) data as Mueller matrix data from an (OHE)experiment [Eq. 1] with magnetic field +/−B and the corresponding zerofield dataset:M _(OHE) ^(±) =M(∈_(B+0)+∈_(±B))  (13)δM ^(±) =M _(OHE) ^(±) −M ₀ =ΔM(∈_(B=0),∈_(±B))  (14)where M₀=M(∈_(Bω0)) is the Mueller matrix of the zero field experiment,and ΔM(∈_(Bω0),∈_(±B)) is the magnetic field induced change of theMueller matrix. This form of presentation is in particular advantageousin case the magnetic field causes only small changes in the Muellermatrix, and provides improved sensitivity to magnetic field dependentmodel parameters during data analysis. Another form of presentation forderived (OHE) data is:δM ₊ ±δM ⁻ =ΔM(∈_(Bω0),∈_(+B))±ΔM(∈_(Bω0),∈_(−B)),  (15)that can be used to inspect symmetry properties of magneto-optic Muellermatrix data, and can help to improve the sensitivity to magnetic fielddependent model parameters during data analysis.Mueller Matrix Data Acquisition (GE)

Spectroscopic ellipsometers can be categorized according to theirpolarization optical components and operation principles, wheredifferent subsets of Mueller matrix elements may be accessible. Forexample Spectroscopic ellipsometers can be classified into twocategories: (i) polarizer-sample+rotating analyzer ellipsometers(PSA_(R)) or rotating-polarizer+sample-analyzer (P_(R)SA)configurations, capable of measuring the upper left 3×3 block of theMueller matrix; and (ii) rotating compensator(s) ellipsometers (RCE) inpolarizer-sample-rotating-compensator-analyzer (PSC_(R)A) orpolarizer-rotating-compensator-sample-analyzer (PC_(R)SA) configuration,capable of measuring the upper left 3×4 or 4×3 block of the Muellermatrix, respectively.

Mathematically all ellipsometers, can be described by the orderedmultiplication of Mueller matrices, corresponding to their consecutiveoptical elements. The Mueller matrices of a polarizer (P), analyzer (A),compensator C(δ) with phase shift coordinate rotation along beam path(R⊖) by an angle ⊖, and of δ, the sample (M) are given by:

$\begin{matrix}{{P = {A = {\frac{1}{2}\begin{bmatrix}1 & 1 & 0 & 0 \\1 & 1 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{bmatrix}}}},{{R(\theta)} = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & {\cos\; 2\;\theta_{j}} & {\sin\; 2\theta_{j}} & 0 \\0 & {{- \sin}\; 2\theta_{j}} & {\cos\; 2\;\theta_{j}} & 0 \\0 & 0 & 0 & 1\end{bmatrix}},{{C(\delta)} = \begin{bmatrix}1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & {\cos\;\delta} & {{- \sin}\;\delta} \\0 & 0 & {\sin\;\delta} & {\cos\;\delta}\end{bmatrix}},{M = \begin{bmatrix}M_{11} & M_{12} & M_{13} & M_{14} \\M_{21} & M_{22} & M_{23} & M_{24} \\M_{31} & M_{22} & M_{33} & M_{34} \\M_{41} & M_{42} & M_{43} & M_{44}\end{bmatrix}},} & (16)\end{matrix}$respectively. Execution of the matrix multiplication characteristic forthe corresponding ellipsometer type shows that, due to the rotation ofoptical elements, the measured intensity at the detector is typicallysinusoidal. Fourier analysis of the detector signal provides Fouriercoefficients, which are used to determine the Mueller matrix of thesample.Data Analysis

Ellipsometry is generally an indirect experimental technique. Therefore,in general, ellipsometric data analysis invokes model calculations todetermine physical parameters in dielectric tensors or the thickness oflayers, for instance. Sequences of homogeneous layers with smooth andparallel interfaces are assumed in order to calculate the propagation oflight through a layered sample, by the 4×4 matrix formalism. To bestmatch the generated data with experimental results, parameters withsignificance physical model parameter in dielectric tensors, layerthicknesses etc. are varied and Mueller matrix data is calculated forall spectral data points, angles of incidence and magnetic fields.During the mean square error (MSE) regression, the generated Muellermatrix data M_(ijk) ^(G), is compared with the experimental Muellermatrix data M_(ijk) ^(B), and their match is quantified by the MSE:

$\begin{matrix}{{MSE} = \sqrt{\left( \frac{1}{{9\; S} - K} \right){\sum\limits_{i = 1}^{4}{\sum\limits_{j = 1}^{4}{\sum\limits_{k = 1}^{S}{\left( {{\left( {M_{i,j,k}^{E} - M_{i,j,k}^{G}} \right)/\sigma}\; M_{i,j,k}^{\cdot E}} \right)2}}}}}} & (17)\end{matrix}$where S, K and σ_(M) _(ij,k) ^(G) denotes the total number of spectraldata points, the total number of parameters varied during the non-linearregression process, the number experimentally determined columns androws of the Mueller matrix and the standard deviation of M{I,j,k},obtained during the experiment, respectively. For fast convergence ofthe MSE regression, the Levenberg-Marquardt fitting algorithm is used.The MSE regression is interrupted when the decrease in the MSE issmaller than a set threshold and the determined parameters areconsidered as best model parameters. The sensitivity and possiblecorrelation of the varied parameters is checked and, if necessary, themodel is changed and the process is repeated. Eventually values forparameters in the mathematical model of the sample being characterizedare arrived at and represent very reliable insight to actual physicalvalues.

It is also mentioned, that is some special cases ellipsometry canprovide results that allow direct analytical solutions for such asconcentration and mobility of charge carriers based on off diagonalJones or Mueller Matrix element value slopes, as a function of anapplied magnetic field. While the typical approach to determining atleast one of the free charge carrier longitudinal and/or transversaleffective masses, and/or concentration, and/or mobility and/or type fromsaid anisotropic values for said at least a partial Jones or MuellerMatrix determining involves use of mathematical regression onto a modelof the sample and ellipsometer or polarimeter system used to evaluatethe Jones or Mueller Matrix elements, it is possible under certaincircumstances to arrive at concentration and mobility of carriers by adirect calculation. This is because in the situation wherein the opticalpath length in a sample, including associated, (eg. Fabry-Perot), cavityforming elements, is a multiple of the wavelength, (ie. Fabry-Perotresonance is achieved, there is a linear relationship between appliedmagnetic field and slope in Off-diagonal Matrix elements. The slope isdifferent for each of the off-diagonal Matrix elements determined, butin all cases depends only on mobility and concentration of chargecarriers. Further, while this determination involves use of slopes intwo such off-diagonal Matrix elements as the applied magnetic field isramped up, it is generally considered that the slope be determined attwo such applied magnetic fields. However, as the off-diagonal Matrixelements vanish when the applied magnetic field is zero, a singleapplied field measurement can sufficient to determine the necessaryslopes.

THz Time-Domain Spectroscopy Based Ellipsometry

Beside THz frequency-domain spectroscopy based ellipsometry discussed inthis Specification, ellipsometry and magneto-optic ellipsometry can beconducted using THz time-domain spectroscopy (THz-TDS), see Sakai,“Terahertz Optoelectronic” Springer-Verlag, (2005). Typically THz-TDS isbased on the Fourier transformation of the time resolved signal ofultra-short (picosecond) laser pulses, revealing the THz spectrum.THz-TDS was developed in the 1980s, and had had its practicalbreakthrough in the 1990s. THz-TDS has since been used to study thebirefringence of a variety of materials in the THz range, as well as theTHz magneto-transmittance for a variety of semiconductors. Polarizationsensitive THz magneto-transmittance based on THz-TDS were reported in1997. THz ellipsometry based on THz-TDS was reported by the Hangyo-groupin 2001, Nagashima & Hangyo, (see App. Phys. Lett., 79, 3017, (2001),and Matsumoto et al., J. J. APP. Phys. 48, (2009) and Matsumoto et al.,Optics Letters, Vol. 36, No. 2, (Jan. 15, 2011), and in 2012 by NeshatOp. Soc., Vol 20, No. 27, (2012)). THz-TDS magneto-ellipsometrymeasurements were reported by Ino et al., (see Phys. Rev. B, 70,(2004)), but external magnetic fields were limited to B approximately0.5 T and Mueller matrix capabilities of the instrument were notdemonstrated.

Search of Patents and Published Applications

A Search of the USPTO Database was conducted for the terms “Optical HallEffect” (OHE) and independently, (1) Ellipsometer, (2) Polarimeter, (3)Terahertz, (4) THZ, in both Issued Patent and Published Applicationcategories. No hits were found. When “Optical Hall Effect” was Searchedon its own, without an accompanying additional term, many hits wereobtained in both categories. However, said hits seem to be referring to“in the alternative” type systems. That is, an invention can use HallEffect or Optical sensing etc. to arrive at a desired result. While notparticularly relevant to the Invention Claimed herein, a few knownPatents that describe Terahertz Ellipsometer Systems or the like areU.S. Pat. Nos. 8,169,611 8,416,408; 8,488,119; 8,705,032 and 8,736,838to Herzinger or Herzinger et al., and which are assigned to the J.A.Woollam Co. Inc., some in conjunction with the Board of Regents of theUniversity of Nebraska. It is also noted that while the presentinvention has generally been practiced by the Inventors herein using aRotating Analyzer Ellipsometer configuration, any Ellispometerconfiguration can be applied including Rotating Polarizer or RotatingCompensator, and combinations thereof. As well, Modulation ElementEllipsometers can also be employed and should be considered within theClaims if not otherwise excluded by Claim language. Although notspecifically directed to Infrared or Terahertz wavelength ranges, Anexample of a Patent covering such a Modulation Element configuration isU.S. Pat. No. 5,657,126 to Duchamrme et al.

Finally in this Background Section of the Specification, it is notedthat terminology used in the Claims regarding Mid-Infrared, FourierTransform Inferared, Far infrared and Terahertz wavelength ranges can beroughly defined as:

-   -   Visual (eg. <8.7 microns);    -   MIR; (eg. 0.7-30 microns);    -   FIR; (eg. 30->350 microns); and    -   THz (eg. (eg. >350-1000 microns).        The relevant literature is not absolutely consistent in said        definitions however and differences in how various publications        define said ranges should not be interpreted to be significant        in disclosure of the present invention.

Even in view of the prior art, need remains for improved systems andmethods of their use that allow the Optical Hall Effect (OHE) to bemonitored at room temperature and relatively low Tesla field strengthsprovided by small permanent magnets.

DISCLOSURE OF THE INVENTION

The present invention comprises a method of evaluating at least some ofthe free charge carrier longitudinal and/or transversal effectivemass(es) and/or concentration and/or mobility and/or free charge carriertype in a sample having a back side and a surface. Said sample can betransparent or semi-transparent, (or even approaching substantiallyopaque beyond a distance from a surface thereinto at wavelength(s)utilized where a detector signal enhancing cavity effect is not requiredto be utilized). Said method comprises the steps of:

-   -   a) providing an ellipsometer comprising:        -   a source of a beam of electromagnetic radiation            characterized by at least one wavelength in a selection from            the group consisting of the:            -   Visual;            -   MIR;            -   FIR; and            -   THz ranges;        -   a polarizer;        -   a stage for supporting a sample, said stage comprising an            adjustable surface that is capable of orienting a sample            placed thereupon via adjustment of at least one selection            from the group consisting of: stage tip, stage tilt and            rotation thereof about an axis projecting substantially            normal to said stage surface, to desired value(s);        -   an analyzer; and        -   a detector of relevant electromagnetic        -   radiation wavelengths.        -   Said method further comprises providing a source of a            magnetic field.            Said method further comprises:    -   b) placing a sample on said stage and adjusting said stage so        that stage tip and/or stage tilt and/or rotation thereof about        an axis projecting substantially normal to said stage surface        are set to desired values, and so that the source of a magnetic        field provides a magnetic field other than parallel thereto at        said surface of said sample;    -   c) while applying the source of a magnetic field to apply a        selected magnitude magnetic field other than parallel thereto at        the surface of said sample, causing said source of        electromagnetic radiation to provide a beam of electromagnetic        radiation of a desired wavelength which is caused to pass        through said polarizer and assume a polarization state, interact        with said sample, pass through said analyzer and enter said        detector which detector produces sample characterizing data.        Said method then continues with:    -   d) from data accumulated by said detector with the system        adjusted as described in steps b) and c), evaluating anisotropic        values for at least a partial Jones or Mueller Matrix; and    -   e) from said anisotropic values for said at least a partial        Jones or Mueller Matrix determining at least one of the free        charge carrier longitudinal and/or transversal effective masses,        and/or concentration, and/or mobility and/or type.

Said method can involve evaluation of said free charge carrierlongitudinal and/or transversal effective masses and/or concentrationand/or mobility and/or type is determined based on data acquired whenthe interaction of said electromagnetic beam of electromagneticradiation with said sample involves transmission thereof through saidsample which is transparent or semi-transparent, (eg. <10¹⁶ cm⁻³ dopingin Silicon), at wavelength(s) utilized. Said method can also involvethat data used in evaluation of said longitudinal and/or transversaleffective masses and/or concentration and/or mobility and/or type isdetermined based on data acquired when the interaction of saidelectromagnetic beam of electromagnetic radiation with said sampleinvolves reflection thereof from said sample which is even approachingsubstantially opaque beyond a distance thereinto from a surface thereofat wavelength(s) utilized, when a detector signal enhancing effect isnot practiced.

Said method can involve said polarizer being set to at least oneadditional polarization setting and/or wherein said source of a magneticfield set to at least one additional magnitude and/or a differentwavelength of electromagnetic radiation different from that originallyutilized is utilized, and additional data is accumulated by saiddetector, which additional data is also used in evaluation said freecharge carrier longitudinal and/or transversal effective masses and/orconcentration and/or mobility and/or type.

Said method can involve data being accumulated with the source providedbeam of electromagnetic radiation set so that it provides at least onesubstantially exact multiple of an optical path length within saidsample.

Said method can involve the source of said magnetic field is a permanentmagnet that provides a magnetic field of about 1 T, or less at thesample surface. It is further within the scope of the present inventionto apply a small electromagnet of a similar Tesla (T) strength in placeof, or in addition to the permanent magnet, but this begins to move awayfrom a benefit of the present invention, that benefit being the abilityto acquire good data with inexpensive easy to use small, (eg. 0.1-0.5 Tor more), permanent magnets.

Said method can involve the sample being transparent or semi-transparentat wavelength(s) utilized, in which said source of said magnetic fieldis a permanent magnet, and wherein a gap exists between an associatedsurface thereof from which a magnetic field other than parallel theretoat said sample surface emanates, and a backside of said sample.

Said method can involve that the beam of electromagnetic radiationinteracts with the sample by at least partially transmitting through itand in which the stage tip and/or tilt is determined based primarily onsetting a desired gap geometry between a surface associated with saidsource of magnetic field and the backside of said sample, said desiredgap, after being determined being secured in place. Said method then cancontinue with said stage tip and/or tilt being secondarily set toprovide an angle-of-incidence and/or plane-of-incidence at which saidbeam of electromagnetic radiation approaches the surface of said sample.It is noted that the associated surface of said magnet can be of themagnet per se. or can be an added element that presents and effectivesurface from which a magnetic field emanates. Stated otherwise, thepresent invention methodology provides that it is convenient to do aprimary tip/tilt to set a desired gap geometry between a surfaceassociated with said source of magnetic field and the backside of saidsample, and then fix said orientational relationship, followed byperforming an additional, secondary, tip/tilt alignment to set thedesired angle-of-incidence and/or plane-of-incidence at which saidellipsometer beam of electromagnetic radiation approaches the surface ofsaid sample.

Said method can, however, involve the beam of electromagnetic radiationinteracting with the sample by reflecting therefrom and in which thestage tip and/or tilt is determined based primarily on orienting thesurface of said sample so that the beam of electromagnetic radiationapproaches said sample surface at a desired angle-of-incidence and/orplane-of-incidence without attention to configuring a gap as alluded toabove.

Said methodology can involve determining nine elements of the MuellerMatrix being evaluated, said nine elements being M11, M12, M13, M21,M22, M23, M31, M32 and M33. Further, said Mueller Matrix elements M12,M13, M21, M22, M23, M31, M32 and M33 can each be divided by the value ofM11 prior to use in evaluating free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type. Ofcourse this is not a limitation of the invention, and more or less thannine can be determined.

A modified recitation of a present invention method of determining atleast some of the free charge carrier concentration and/or mobility in asample, said sample having a back side and a surface and beingtransparent or semi-transparent (or even approaching substantiallyopaque beyond some distance thereinto from a surface thereof when adetector enhancing cavity effect is not utilized), at wavelength(s)utilized, comprises the steps of:

-   -   a) providing an ellipsometer comprising:        -   a source of a beam of electromagnetic radiation            characterized by at least one wavelength in a selection from            the group consisting of the:            -   Visual;            -   MIR;            -   FIR; and            -   THz ranges.                Said ellipsometer system further comprises:    -   a polarizer;    -   a stage for supporting a sample, said stage comprising an        adjustable surface that is capable of orienting a surface of a        sample placed thereupon via adjustment of at least one selection        from the group consisting of: stage tip, stage tilt and rotation        thereof about an axis projecting substantially normal to said        stage surface, to desired value(s); and    -   a detector of relevant electromagnetic radiation wavelengths;        and    -   further providing a source of a magnetic field.        Said method continues with:    -   b) placing a sample on said stage and adjusting said stage so        that stage tip and/or stage tilt and/or rotation thereof about        an axis projecting substantially normal to said stage surface        are set to desired values, and so that the source of a magnetic        field provides a magnetic field other than parallel thereto at        said surface of said sample;    -   c) while applying the source of a magnetic field to apply a        selected magnitude magnetic field other than parallel thereto at        the surface of said sample, causing said source of        electromagnetic radiation to provide a beam of electromagnetic        radiation comprising at least one wavelength of a substantially        exact multiple of a an optical path length in said sample, and        which beam is caused to pass through said polarizer and assume a        polarization state, interact with said sample, pass through said        analyzer and enter said detector, which detector produces sample        characterizing data;    -   d) from data accumulated by said detector with the system        adjusted as described in steps b) and c), evaluating anisotropic        values for at least a partial Jones or Mueller Matrix; and    -   e) from said anisotropic values for said at least a partial        Jones or Mueller Matrix determining at least one of the free        charge carrier concentration and/or mobility by direct        calculation rather than by a mathematical regression procedure.

The above described methodology can involve using a stage for supportinga sample that functionally comprises:

a) an interface plate comprising said sample supporting stage;

b) a magnetic casing plate for positioning at least one magnet withrespect to said sample supporting stage, through which said magneticcasing plate said interface plate projects.

Importantly, said stage for supporting a sample further comprises:

c) a mechanism for adjusting the tip and/or tilt of said stage withrespect to a surface associated with said at least one magnet such thatsaid surface associated with said at least one magnet is substantiallyparallel to the back of a sample placed on said sample supporting stage.In use said stage for supporting a sample can provide that the magneticcasing plate and interface plate are offset from one another to providea gap therebetween, which gap contributes to formation of a cavityeffect wherein at least some electromagnetic radiation directed at saidsample by said source of a beam thereof passes through said sample,reflects from said surface associated with said at least one magnet andre-enters said sample.

Said magnetic casing plate can comprise two magnet holders optionallyinterconnected by a magnetic material, (eg. iron), support bar.

It is to be understood that the present invention also includes thestage per se. for supporting a sample having a back side and a surfaceas just described above, and which comprises:

a) an interface plate comprising a sample supporting stage;

b) a magnetic casing plate for positioning at least one magnet withrespect to said sample supporting stage;

c) a mechanism for adjusting the tip and/or tilt of said stage withrespect to a surface associated with said at least one magnet, such thatsaid surface associated with said at least one magnet is substantiallyparallel to the back side of a sample placed on said sample supportingstage; such that in use said magnetic casing plate and interface plateare offset from one another and adjusted by said mechanism for adjustingthe tip and/or tilt of said stage to provide a gap therebetween thatestablishes a resonance cavity in which at least some electromagneticradiation caused to be incident on the sample surface transmits throughsaid sample and reflects from said surface associated with said magnetback into said sample. Said stage further comprises a mechanism forfixing the described relationship between said magnetic casing plate andinterface plate, and then allowing the tip/tilt capability be used toadjust an ellipsometer beam angle and/or plane of incidence thereto.

Said stage can be characterized by at least one selection from the groupconsisting of:

a) said magnetic casing plate comprises two magnet holders, optionallyinterconnected by a magnetic material support bar;

b) said gap is set by a mechanism, (eg. a motor, typically a computerdriven stepper motor), that adjusts the relative orientation betweensaid magnetic casing plate and said interface plate;

c) said gap is formed by placing spacer material between the back ofsaid sample and a surface of said stage upon which said sample isplaced;

d) said gap is formed by at a spacer comprising at least one layer oftape between the back of said sample and a surface of said stage uponwhich said sample is placed.

Another modified recitation of present invention methodology fordetermining at least one of the free charge carrier concentration and/ormobility in a sample, said sample having a back side and a surface andbeing transparent or semi-transparent or substantially opaque at somedistance thereinto from a surface thereof, (when a detector signalenhancing cavity effect is not utilized), thereinto at wavelength(s)utilized, said method comprising the steps of:

-   -   a) providing an ellipsometer comprising:    -   a source of a beam of electromagnetic radiation characterized by        at least one wavelength selected from the group consisting of:        -   Visual;        -   MIR;        -   FIR; and        -   THz;    -   ranges;    -   a polarizer;    -   a stage for supporting a sample;    -   an analyzer; and    -   a detector.        Said methodology continues with:    -   b) placing a sample on said stage and adjusting said stage so        that stage tip and/or stage tilt and/or rotation thereof about        an axis projecting substantially normal to said stage surface        are set to desired values, and so that the source of a magnetic        field provides a magnetic field other than parallel thereto at        said surface of said sample, and/or adjusting the source of a        magnetic field which is oriented to provide a magnetic field        other than parallel thereto at said surface of said sample, to        achieve a desired value of magnetic field at said sample        surface,    -   c) while applying the source of a magnetic field to provide a        selected magnitude magnetic field other than parallel thereto at        the surface of said sample, causing said source of        electromagnetic radiation to provide a beam of electromagnetic        radiation which is caused to pass through said polarizer and        assume a polarization state, interact with said sample, pass        through said analyzer and enter said detector, which detector        produces sample characterizing data;        And said method further involves:    -   d) from data accumulated by said detector with the system        adjusted as described in steps b) and c), evaluating anisotropic        values for at least a partial Jones or Mueller Matrix; and    -   e) from said values for said at least a partial Jones or Mueller        Matrix determining at least one of the free charge carrier        concentration and/or mobility.

In any of the present invention methodology the data can be acquired atroom temperature. This is a benefit over prior art approaches whichrequire temperatures such as achieved by applying liquid helium.

Further, in any present invention methodology the ellipsometer canfurther comprise at least one compensator between the source of a beamof electromagnetic radiation and the detector. (It is noted that thepresence thereof enables acquiring sufficient data to arrive at a fullsixteen (16) member Mueller matrix).

As alluded to, said methodology as recited above involves at least apartial Mueller matrix being determined and, of the Mueller Matrixelements M11, M12, M13, M21, M22, M23, M31, M32 and M33 that can bedetermined, at least M11, and at least one of M23 and M32 are. Saidapproach to determining values for M11 and at least one of M23 and M32can be distinguished in that data is determined by a selection from thegroup consisting of:

-   -   placing said sample on said stage for supporting a sample with        the back side thereof in contact with said stage and obtaining a        first set of data, then flipping said sample so that it's        surface is in contact with said stage and obtaining a second set        of data; and    -   first placing the north pole of a permanent magnet near to the        sample and obtaining a first set of data, and then placing a        south pole of the same or another magnet so that it is near the        sample and obtaining a second set of data,        which is followed by subtracting said second set of data from        said first, or vice-versa, for each of the resulting M1, and at        least one of said resulting M23 and M32 Mueller Matrix elements        determined, and wherein each determined M23 and M32 is divided        by the resulting M11, prior to using said resulting at least one        of the resulting M23 and M32 values as data upon which to        regress a model of said sample that includes free charge carrier        longitudinal and transversal effective masses, concentration,        mobility and type, thereby allowing their evaluation.        Said methodology and can further involve at least one of M13 and        M31 also being determined by the same procedure of obtaining a        first set of data with the sample back side in contact with said        stage and then flipping said sample over so that it's surface is        in contact with said stage and obtaining a second set of data;        or by first placing the north pole of a permanent magnet near to        the sample and obtaining a first set of data, and then placing a        south pole of the same or another permanent magnet so that it is        near the sample and obtaining a second set of data.        As before, the method continues with subtracting said second set        of data from said first, or vice-versa, for each of the        resulting M11, and at least one of said resulting M13 and M31        Mueller Matrix elements determined, prior to using said        resulting at least one of M23 and M32 and at least one of M13        and M31 values as data upon which to simultaneously regress a        model of said sample that includes free charge carrier        longitudinal and transversal effective masses, concentration,        mobility and type, thereby allowing their evaluation.

Likewise, at least a partial Mueller matrix can determined and, of theMueller Matrix elements M11, M12, M13, M21, M22, M23, M31, M32 and M33that can be determined, at least M11, and at least one of M13 and M31are. Said approach to determining values for M11, and at least one ofM13 and M31 is distinguished in that data is determined by a selectionfrom the group consisting of:

-   -   placing said sample on said stage for supporting a sample with        the back side thereof in contact with said stage and obtaining a        first set of data, then flipping said sample so that it's        surface is in contact with said stage and obtaining a second set        of data; and    -   by first placing the north pole of a permanent magnet near to        the sample and obtaining a first set of data, and then placing        the south pole of the same or another magnet so that it is near        the sample and obtaining a second set of data. (Note, where a        single permanent magnet is used this amounts to “flipping” it        over. However, any approach to modulating the effective magnetic        field “seen” by a sample between the obtaining of data sets is        within the scope of the present invention. That is, specific        examples given are not to be considered to be of a limiting        nature as regards the actual motion practiced. Because it is        convenient, a preferred approach might involve that a single        magnet be literally “flipped” over to cause a change from a        North to South pole being closer to a sample, or vice versa, is        practiced between acquiring the identified two data sets. It is        also possible though, to place two magnets on a slider, one with        a North pole and one with a South pole oriented so that they can        be made to face toward the sample in use. A lateral sliding        motion of said slider then places one and then the other of said        north and south poles nearer the sample between acquiring two        different data sets. Any configuration which allows a        modulation, (not even necessarily a complete pole type change),        of a magnetic B Field near a sample is to be considered within        the scope of possibilities as regards how to arrive at two data        sets, (or modulate a signal).        Said methodology then involves subtracting said second set of        data from said first, or vice-versa, for each of the resulting        M11, and at least one of said resulting M23 and M32 Mueller        Matrix elements determined, and wherein each determined M13 and        M31 is divided by M11, prior to using said resulting at least        one of M13 and M31 values as data upon which to regress a model        of said sample that includes free charge carrier longitudinal        and transversal effective masses, concentration, mobility and        type, thereby allowing their evaluation.        Further, said methodology can involve at least one of M23 and        M32 also being determined by the same procedure of data being        determined by the same procedure of data being determined by        obtaining a first set of data with the sample back side in        contact with said stage and then flipping said sample over so        that it's surface is in contact with said stage and obtaining a        second set of data; or again by first placing the north pole of        a permanent magnet near to the sample and obtaining a first set        of data, and then flipping the magnet so that the south pole        thereof is near the sample and obtaining a second set of data,        and then subtracting said second set of data from said first for        each of the resulting M11, and at least one of said resulting        M23 and M32 Mueller Matrix elements determined, prior to using        said resulting at least one of M23 and M32 and at least one of        M23 and M32 values as data upon which to simultaneously regress        a model of said sample that includes free charge carrier        longitudinal and transversal effective masses, concentration,        mobility and type, thereby allowing their evaluation.

Said methodology can involve the sample supporting stage being adjustedto be at a desired distance from a magnet, by placing at least one layerof spacer material, (eg. Tape), between said sample supporting stage andthe sample supported thereby, or by use of a motor to achieve a desiredcavity gap. Any approach to achieving a desired cavity gap geometry,however is within the scope of the present invention.

It is noted that the foregoing methodology can involve that thepermanent magnet utilized provides a field strength at the sample ofbetween 0.1-0.5 or more Tesla.

Another recitation of present the invention methodology of enhancing thecapability of determining free charge carrier concentration and mobilityin a sample having a back side and a surface, said sample beingtransparent or semi-transparent at wavelength(s) utilized, said methodcomprising the steps of:

-   -   a) providing an ellipsometer comprising:        -   a source of a beam of electromagnetic radiation            characterized by at least one wavelength in a selection from            the group consisting of the:            -   Visual;            -   MIR;            -   FIR; and            -   THz; ranges;        -   a polarizer;        -   a stage for supporting a sample;        -   an analyzer; and        -   a detector;    -   and a source of a magnetic field having a surface associated        therewith and which is oriented to provide a magnetic field        other than parallel thereto at said surface of said sample.        As before, said method continues with:    -   b) placing a sample on said stage and adjusting said stage so        that stage tip and/or stage tilt and/or rotation thereof about        an axis projecting substantially normal to said stage surface        are set to desired values, and so that the source of a magnetic        field provides a magnetic field other than parallel thereto at        said surface of said sample, and/or further adjusting the source        of a magnetic field so that it is oriented to provide a magnetic        field other than parallel thereto at said surface of said sample        of a desired value;    -   c) while applying the source of a magnetic field to apply a        magnetic field other than parallel thereto at the surface of        said sample or a desired value, causing said source of        electromagnetic radiation to provide a beam of electromagnetic        radiation comprising at least one wavelength of substantially an        exact multiple of an optical path length in said sample, which        beam is caused to pass through said polarizer and assume a        polarization state, interact with said sample, pass through said        analyzer and enter said detector, which detector produces sample        characterizing data.        Said method then further involves:    -   d) from data accumulated by said detector with the system        adjusted as described in steps b) and c), evaluating anisotropic        values for at least a partial Jones or Mueller Matrix; and    -   e) from said values for said at least a partial Jones or Mueller        Matrix directly determining at least one of the free charge        carrier concentration and/or mobility.        Said just recited methodology is, however, distinguished in        that, while data is being accumulated by said detector, a gap is        caused to exist between at least one selection from the group        consisting of:    -   1) said sample backside and the sample supporting stage; and    -   2) said sample supporting stage and said surface associated with        said source of a magnetic field which is oriented to provide a        magnetic field other than parallel thereto at said surface of        said sample of a desired value;        such that a cavity is formed in which at least some        electromagnetic radiation in the beam thereof directed at said        sample by said source of a beam of electromagnetic radiation        passes through said sample, and is coherently reflected back        thereinto by said surface associated with said source of a        magnetic field.

Said just recited methodology can involve the gap being caused to existby placing spacer material between said sample back side and said samplesupporting stage, and/or in which the gap is caused to exist by, forinstance, application of, for instance, a motor applied between aninterface plate that comprises said sample supporting stage, and amagnet casing plate that comprises said surface associated with saidsource of a magnetic field which is oriented to provide a magnetic fieldother than parallel thereto at said surface of said sample.

In any of the recited methodology the polarizer can be a rotatablepolarizer and the analyzer can be a rotating analyzer.

In any of the recited methodology the magnetic field which is appliedother than parallel thereto at the surface of said sample can preferablyapplied substantially, or exactly perpendicular to said sample surface.This preference is not limiting however.

As mentioned earlier, the methodology can further comprise providing acompensator between said source and detector to increase the capabilityof determining more complete Mueller matrix element determining data.

In most applications of practicing present invention methodologymathematical regression is applied to Jones or Mueller matrix elementsto arrive at the desired values, however, in some special cases directmathematical calculation to Jones or Mueller matrix elements can bepracticed to arrive at the desired values for concentration and/ormobility of charge carriers present.

As it is important to be clear regarding present invention ellipsometeror the like systems that can be applied in practice of the presentinvention methodology, it is here presented that such systems comprise:

a polarization state generator;

a stage for supporting a sample, said stage having a substantially flatsurface; and

a polarization state detector.

(Note, the terminology “polarization state generator” refers to whatproceeds a sample and sets a polarization state in a beam ofelectromagnetic radiation caused to impinge on a sample at anangle-of-incidence and plane-of-incidence values, and “polarizationstate detector” refers to follows a sample and serves to develop databased on electromagnetic radiation entering thereinto).Continuing, in use said polarization state generator is caused to directa polarized beam of electromagnetic radiation to interact with a sampleon said stage for supporting a sample, which after said interactionpresents as a beam of electromagnetic radiation that enters saidpolarization state detector, that in response produces samplecharacterizing data.

Importantly, to stress the importance of the point, it is again notedthat said just recited present invention ellipsometer or the like systemis distinguished in that said stage for supporting a sample isfunctionally a part of a cavity, that directs electromagnetic radiationthat passes through a transparent or semi-transparent sample supportedupon said stage having a substantially flat surface to be reflected backinto said transparent or semi-transparent sample, such that when samplecharacterizing data is being accumulated by said polarization statedetector, it is enhanced over what it would be otherwise as a result ofcoherent interaction in said transparent or semi-transparent samplebetween electromagnetic radiation incident thereupon provided by saidpolarization state generator, and electromagnetic radiation thatreflects back into said transparent or semi-transparent sample as aresult of said resonance effect, a resulting coherent combination ofsaid two identified contributions of electromagnetic radiation in saidsample then comprising said beam that enters said polarization statedetector.

Said system as just recited can further comprise a magnet casing plate,such that in use a magnet can be secured thereto in a manner such that amagnetic field directed other than parallel thereto at the samplesurface is presented to said sample, and which magnet casing plate andsubstantially flat surface associated with said magnet can be adjustedto be substantially parallel thereto at said substantially flat surfaceof said stage.And, said system as just recited can further comprise a mechanism thatenables aligning the substantially flat surface of said stage and thesubstantially flat surface associated with said magnet so that they aresubstantially parallel to one another by a tip/tilt procedure. Saidpresent invention provides that it can be said stage for supporting asample that is caused to undergo said tip/tilt procedure to align thesubstantially flat surface associated with said magnet substantiallyparallel to the stage substantially flat surface, and/or it can be saidsubstantially flat surface associated with said magnet that is caused toundergo said tip/tilt procedure to align the substantially flat surfaceassociated with said magnet substantially parallel to the stagesubstantially flat surface.

In use said system as just described can provide that said substantiallyflat surface associated with said magnet is caused be alignedsubstantially parallel to the stage substantially flat surface, thensaid resulting orientation is secured in place, followed by saidtip/tilt procedure being practiced primarily to align said stagesubstantially flat surface so that desired angle-of-incidence and/orplane-of-incidence of said beam of electromagnetic radiation caused tobe directed at said sample by said polarization state generator, is/areachieved. This provides insight as to how the inventors have used thedescribed system to achieve results.

It is also noted that said system can be characterized in that theresonance effect is enhanced by placing spacer material between thestage for supporting a sample and a sample supported thereby.

It is further noted that while the resonance cavity effect is not easilyachieved for samples which are effectively opaque below some distancefrom the sample surface, (eg. 50 microns is to be considered a typicaldistance), the described system can still be applied allow sampleinvestigation within said typical 50 microns via a beam ofelectromagnetic radiation which is caused to reflectively interact witha sample surface, to produce sample characterizing data. It is alsonoted that where sample characterizing data is obtained without use ofdata enhancing cavity effects, samples analyzed can be transparent,semi-transparent or even opaque below some distance into said samplefrom a surface thereof. The later situation requires that reflectiveelectromagnetic beam and sample interaction be applied of course, as abeam cannot transmit through a sample with is opaque at wavelengthsused. This is not a limitation where transparent or semi-transparentsample are analyzed at wavelengths utilized. Note, different wavelengthsprovide different characteristics as regards if a sample is generally“transparent” or “semi-transparent”. This is especially true forsemiconductors. Therefore selection of an appropriate wavelength in theVisible, Mid-Infrared, Far Infrared or THz range is important wherecavity data enhancement effects are to be utilized. It is emphasizedthat this comprises a major benefit provided by the present invention.Electromagnetic radiation transmitted through and reflected back into asample provides significant benefits. Further, it is to be understoodthat a present invention reference to wavelength(s) being “at least onesubstantially exact multiple of an optical path length in a sample” isto be interpreted wherein said wavelength(s) is/are determined when asample is in a cavity, which cavity geometry affects what thewavelength(s) is/are. That is, for the purposes of the present inventionthe term “sample” is to be considered in the context of the cavity ofwhich it is a part and it is the whole thereof that is defining of saidwavelength(s). This should be kept in mind while considering Claimlanguage. And, while opaque samples can be analyzed according to theteachings herein in reflection mode, data enhancing resonance effectsare practical only where a sample is at least semi-transparent.

In view of the foregoing, it is considered that there are manyPatentable aspects of the present invention, but in particular it isbelieved that use of a cavity to reflect electromagnetic radiation backinto a transparent or semi-transparent sample after it passestherethrough, for the purpose of enhancing an ellipsometer beam signalthat enters an ellipsometer system detector, especially in combinationwith use of a small, (eg. 0.1-0.5 T or more, but usually <1.0),permanent magnet to provide a B Field at a sample surface to investigatea sample via Optical Hall Effect methodology, provides new, non-obviousand useful invention.

It is further mentioned, and will be pursued in additional Applications,that the use of a cavity to reflect electromagnetic radiation back intoa transparent or semi-transparent sample after it passes therethrough,for the purpose of enhancing an ellipsometer beam signal that enters anellipsometer system detector, is applicable to use in ellipsometer orthe like systems even when the Optical Hall Effect is not beinginvestigated. That is, operation of any ellipsometer or the like systemcan be enhanced by application of a reflecting cavity. Further, such acavity can be modulated as regards its size, (eg. depth), during sampleinvestigation and thereby modulate the signal the ellipsometer or thelike system detector receives. This allows, for instance, anellipsometer polarizer and analyzer to remain fixed during dataacquisition while still deriving the benefits of a modulated beam.

The invention will be better understood by reference to the DetailedDescription Section of this Disclosure, in combination with theDrawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1a shows a block diagram of an integrated VIS-MIR and FIR-THz (OHE)instrument.

FIGS. 1b and 1c show the VIS-MIR and FIR-THz subsystems in more detail.

FIG. 1d provides a reference for a general THz based ellipsometersystem.

FIGS. 1d ′, 1 d″ and 1 d″′ show demonstrative systems for placingmagnets near a sample stage as in FIG. 1 d.

FIG. 1e shows another embodiment of a THz ellipsometer system developedby the J.A. Woollam Co.

FIG. 1e ′ demonstrates that the stage in FIG. 1e can be rotated toaffect an angle of incidence of a beam of electromagnetic radiationthere-approaching.

FIG. 1f shows better detail of a sample adjacent to a reflective Cavity.

FIGS. 1g and 1h demonstrate a non-limiting stage that allows tip/tilt tobe accomplished for the purpose of adjusting a cavity geometry, and foradjusting angle and plane of incidence of an ellipsometer beam withrespect to a sample surface.

FIGS. 2a-2e there is shown a stage for supporting a sample that issuitable for use in the preferred embodiment of the present invention.

FIGS. 3a and 3b , there is represented in FIG. 3a , a three (3) bounceOdd Bounce image rotating system (OBIRS).

FIGS. 3c-3g show various designs for rotating compensator systems.

FIGS. 4a and 4b show Mueller Matrix data obtained using the presentinvention which comprises the stage of FIGS. 2a-2e that incorporates apermanent magnet and which is applied at room temperature.

FIG. 4c shows a 4×4 Mueller Matrix.

FIG. 4d shows M12/M11, M21/M11 and M33/M11 Mueller Matrix componentsobtained with no B Field applied.

FIG. 4e shows Mueller Matrix Elements M13/M11, M31/M11, M23/M11 andM32/M11 obtained with a B field applied, and wherein the data shown isthe difference between that obtained when the Magnet is placed with theNorth Pole facing one direction and then the other.

FIG. 5 is included to indicate that it is optimum to provide VIS-MIR andFIR-THz sources that provide output which overlaps in the range of about1.0 to 1.4 THz.

FIG. 6 demonstrates displaying data (DIS) provided by a Detector (DET).

DETAILED DESCRIPTION

Turning now to FIG. 1a there is shown a block diagram of an integratedVIS-MIR and FIR-THz (OHE) instrument. Said integrated (OHE) instrumentcontains multiple light sources and detectors, and covers a spectralrange from 3 cm⁻¹ to 7000 cm⁻¹ (0.1-210 THz or 0.4-870 meV). It is notedthat both ellipsometer sub-systems can be operated without themagneto-cryostat sub-system (MCS) in a variable angle of incidenceellipsometry mode. The angle of incidence is defined as the anglebetween the surface normal of the sample and the incoming beam.

The present invention, in its preferred embodiment, is an integratedVIS-MIR and FIR-THz (OHE) instrument as identified in FIG. 1a , howeversaid preferred embodiment is suitable for use at room temperature and Bfields produced by relatively small permanent magnet(s) in an equivalentto the (MCS) subsystem which will be described with respect to FIGS. 2a-2 e.

Continuing, FIGS. 1b and 1c show the VIS-MIR and FIR-THz subsystems inmore detail.

FIG. 1d provides a reference for a general THz based ellipsometersystem, showing:

a source (BWO) of terahertz electromagnetic radiation;

a first rotatable polarizer (WGP1);

a first rotatable element (RE1);

a stage (STG) for supporting a sample (S);

a second rotatable element (RE2);

a second rotatable polarizer (WGP2); and

a detector (DET) of terahertz electromagnetic radiation.

It should be appreciated that a combination of a source (BWO) ofterahertz electromagnetic radiation a first a rotatable polarizer (WGP1)and a first rotatable element (RE1) can be referred to as a polarizationstate generator, while a combination of a second rotatable element (RE2)and a second rotatable polarizer (WGP2) and a detector (DET) ofterahertz electromagnetic radiation considered as a polarization, statedetector. FIGS. 1d ′, 1 d″ and 1 d″′ show that a magnet can be placedwith respect to a stage (STG) for use in practicing the Optical HallEffect (OHE) methodology described elsewhere herein. FIGS. 1d ′ and 1 d″suggest flipping the magnet and FIG. 1d ″′ shows two magnets on asupport which can be positioned, (slid or rotated), to provide a North(N) or South (S) pole as desired or as an approach to modulation ofsignal during data acquisition. It is further noted that the Sample (S)could also be rotated during data acquisition to provide modulation. Achopper could be applied to provide a similar effect. As well, anywherea magnet is applied it could be of a modulated strength, perhaps bybeing combined with an electromagnet.

FIG. 1e shows another embodiment of a THz ellipsometer system developedby the J.A. Woollam Co. FIG. 1e ′ demonstrates that the stage in FIG. 1ecan be rotated to effect an angle of incidence of a beam ofelectromagnetic radiation there-approaching FIG. 1e which shows apreferred embodiment of the present invention Terahertz Ellipsometersequentially system comprising:

a source (BWO) of terahertz electromagnetic radiation;

a first rotatable polarizer (WGP1):

a stage (STG) for supporting a sample (S);

a second rotatable polarizer (WGP2);

a detector (DET) of terahertz electromagnetic radiation.

Said terahertz ellipsometer or polarimeter system further comprises afirst rotating element (REI) and second rotating element (RE2) betweensaid source and detector of electromagnetic radiation.

In use said source of terahertz electromagnetic radiation directs a beam(BI) of terahertz frequency electromagnetic radiation of a fundamentalfrequency to pass through said first rotatable polarizer, then reflectfrom a sample (S) placed on said stage (STG) for supporting a sample,then pass through said second rotatable polarizer, and as output beam(BO) enter said detector of electromagnetic radiation as output beam(BO), wherein said beam also passes through said first rotating element(RE1) and second rotating element (RE2).

In more detail FIG. 1e shows a more detailed preferred presentlydisclosed terahertz ellipsometer sequentially system comprising:

-   -   a backward wave-oscillator (BWO);    -   an optional frequency multiplier (FM);    -   an optional first concave parabolic mirror (PM1),    -   an optional reflecting means (M1);    -   a first rotatable wire grid polarizer (WGP1);    -   an optional second concave parabolic mirror (PM2);    -   a rotating wire grid polarizer (RWGP);    -   a stage for (STG) supporting a sample (S);    -   a rotating retarder (RRET) (comprising first, second, third and        fourth elements as shown in FIGS. 3c-3g ); said FIG. 3c        demonstrating a preferred arrangement of:        -   first (RP), second (RM1), third (RM2) and fourth (RM3)            reflective elements from each of which, in use, an            electromagnetic beam reflects once,        -   said first reflective element (RP) being prism (RP) which            receives a beam through a first side thereof and exits a            reflected beam through a third side thereof,        -   said reflection being from a second side thereof oriented at            prism forming angles to said first and third sides; said            elements (RP) (RM1) (RM2) (RM3) being oriented with respect            to one another such that the locus of the beam reflecting            from the second side of said prism approaches said second            reflective side thereof at an angle equal to or greater than            that required to achieve total internal reflection within            said prism (RP),    -   and such that the locus of beam reflected from the fourth        element in the sequence of elements is substantially co-linear        and without deviation or displacement from the locus of the beam        received by the first element in said sequence of elements,    -   an optional third concave parabolic mirror (PM3);    -   a second rotatable wire grid polarizer (WGP2);    -   an optional fourth concave parabolic mirror (PM4); and    -   a Golay cell detector (DET).

Assuming optional elements are present, in use said backward waveoscillator (BWD) directs a beam of terahertz frequency electromagneticradiation of a fundamental frequency to said frequency multiplier (FM),from which frequency multiplier (FM) a beam comprising a desiredfrequency is caused to be reflected from said first concave parabolicmirror (PMI) as a substantially collimated beam, said substantiallycollimated beam then being directed to reflect from said reflectingmeans (MI) and pass through said fist rotatable wire grid polarizer(WGP1) and reflect from said second concave parabolic mirror (PM2)through said rotating wire grid polarizer (RWGP), then reflect—from asample (S) placed on said stage (STG) for supporting a sample, then passthrough said rotating retarder (RRET), reflect from said third parabolicmirror (PM3), pass through said second rotatable wire grid polarizer(WGP2), then reflect from said fourth concave parabolic mirror (PM4) andenter said Golay cell detector (DET).

FIG. 1e ′ shows that that the FIGS. 1d and 1e terahertz ellipsometersystem can further comprise means for rotating, as a unit, said:

-   -   stage (STG) for supporting a sample (S);    -   rotating retarder comprising first (RP), second (RM1), third        (RM2) and fourth (RM3) elements;    -   third concave parabolic mirror (PM3);    -   second rotatable wire grid polarizer (WGP2);    -   fourth concave parabolic mirror (PM4); and    -   Golay cell detector (DET);        about a vertical axis centered at a midpoint of said stage (STG)        for supporting a sample (S) such that the angle of incidence (6)        at which said beam of terahertz frequency electromagnetic        radiation approaching from said rotating wire grid polarizer        (RWGP), and the angle of reflection (e) of said beam from said        sample (S) placed on said stage (STG) for supporting a sample,        can be adjusted.

FIG. 1e is to also be interpreted to, in addition, or as an option,enable said terahertz ellipsometer system to further comprise means forrotating, as a unit, said:

backward wave oscillator (BWO);

frequency multiplier (FM) if present;

first concave parabolic mirror (PMI) if present;

reflecting means (MI) if present;

rotatable wire grid polarizer (WGPI);

second concave parabolic mirror (PM) if present;

rotating wire grid polarizer (RWGP);

about a vertical axis centered at a midpoint of said stage (STG) forsupporting a sample (S) such that the angle of incidence (9) at whichsaid beam of terahertz frequency electromagnetic radiation approachingfrom said rotating wire grid polarizer (RWGP), and the angle ofreflection (e) of said beam from said sample (S) placed on said stage(STG) for supporting a sample, can be adjusted.

In practice either the components on the Source (BWO) and/or Detector(DET) side of the stage (STG), along with the stage can be rotated toset an Angle-of-Incidence of a Terahertz beam onto a sample.

The terahertz ellipsometer system can further comprise a beam chopper(CHP), said beam chopper (CHP) being of any functional design, buttypically being a rotating wheel with a plurality of openings thereinthrough which the terahertz electromagnetic radiation beam can pass,said chopper being placed the locus of the terahertz electromagneticradiation beam at some point between said backward wave oscillator andsaid Golay cell detector, said wheel being made from high densitypolyethelyene. Note the position of the chopper (CH) in FIG. 1e isdemonstrative, not limiting. The chopper (CHP) can be located at anyfunctional location in the terahertz ellipsometer system.

It is noted that said terahertz ellipsometer system is typicallyoriented to mount samples (B) to said stage (8TG) for supporting asample so that said sample (S) is in a vertical plane as observed inlaboratory coordinates. FIG. 1e ′ shows a system that allows saidterahertz ellipsometer system to orient the stage (STG) for supporting asample (8) in a horizontal plane. Note that the stage (STG) forsupporting a sample (S) is oriented to support a sample in a horizontalplane and in which the beam is directed thereto via left and rightvertical sequences, each of first (FLS/FRS) second (BLB/BRB) and third(TLS/TRS) elements, such that the terahertz frequency electromagneticbeam exiting said rotating wire grid polarizer (RWGP) reflects from thefirst “left side element (FLS) to the second left side” element (BLS),then to the third right side, element (TRS), from which it is directedto reflect from a sample (S) placed on the stage (STG) in a horizontalplane toward the third left side element (TLS), which reflects said beamto the second right: side element (BRS) toward said first right sideelement (FRB), from which said beam is directed into said rotatingretarder (RRET), (see FIG. 1e ).

FIG. 1f shows demonstrative detail of a Sample (S) on a Stage (STG),(shown as “split” to avoid it's affecting a beam which passes through aSample (SAM)), adjacent to a Cavity (CAV) having a reflective surface(REF). With reference to FIG. 2b it can be appreciated that an effectiveCavity (CAV) can be formed between a magnetic casing plate (MCP) andInterface Plate (IP), and a Motor (SP) applied to control the geometryof the Cavity (CAV). Note that the effect of the Cavity (CAV) andreflective surface (REF) thereof, causes an enhanced coherent signal toexit the Sample (S) and proceed toward the Detector (DET) of anellipsometer system utilized. It is also noted that representativematerials from which to construct reflective surfaces (REF) includemetals, highly doped semiconductors (10¹⁸ cm⁻³), Bragg Dielectricreflectors, total internal reflection condition systems, and long cavitytunnel reflectors.

FIGS. 1g and 1h are included for general insight and are not limiting.FIG. 1g indicates that a Cavity (CAV) is formed between the lowersurface of a Stage (STG) for supporting s Sample, (as generally shownin, for instance, FIG. 1d ), and a Reflector (REF) upper surface. Oneway to enable adjusting the relative orientations of said Stage (STG)and Reflector (REF) is to place Screws (SCR) at each corner of theReflector (R) which are secured so that rotation thereof causes theScrews to extend or retract with respect to said Reflector (RFE). TheScrews (SCR) are affixed to the Stage (STG) via Securing Means (SM) thatallow Screw rotation therewithin, while maintaining a fixed position ofthe end thereof with respect to said Stage (STG). It should be apparentthe Stage (STG) can be effectively rotated in Tip and Tilt directions byselective rotation (note the arrows showing Stage (STG) Tip and Tilt) ofthe Screws until a desired Cavity Geometry is achieved. With a Cavity(CAV) geometry achieved as demonstrated, a further Stage (STG) Tip/Tiltcan be achieved as suggested by FIG. 1e ′. Again, FIGS. 1f-1h are notlimiting. They simply serve to give insight to the need to be able toadjust a Stage (STG) for two purposes. One is to provide a desiredCavity (CAV) geometry and the other is the to enable adjustment of theAngle-of-Incidence an ellipsometer beam makes with respect to a Sample(SAM) surface.

Turning now to FIGS. 2a-2e there is shown a stage system for supporting(STG) a sample (S) that is suitable for use in the present invention,(Note FIG. 2a provides exemplary, not limiting dimensions of a preferredstage). Said stage system can be described as being comprised of:

-   -   a) a mechanism for adjusting tip and/or tilt of a surface of a        sample (S) placed on a surface of said stage (STG) for        supporting a sample (S);    -   b) an interface plate (IP) comprising said stage for supporting        a sample, and which is controlled by said mechanism for        adjusting the tip and/or tilt of a surface of a sample (S)        placed thereon on a surface of said stage;    -   c) a magnetic casing plate (MCP) comprising at least one magnet        holder (MH1) (MH2) for securing at least one magnet thereto,        said magnetic casing plate (MCP) and interface plate (IP) being        off-settable from one another and controlled in relative        orientation with respect to one another by, for instance, a        motor, and wherein a selection form the group consisting of: one        magnet holder (MH1); and two magnet holders (MH1) (MH2), which        can be, but do not necessarily need to be so, interconnected by        a magnetic material. (eg. Iron), support bar (ISB) as shown in        FIG. 2c , and in which the sample supporting stage (STG) can be        adjusted to be at a desired distance from and in a desired        orientation with respect to said magnet(s) (MAG1) (MAG2) in said        holder(s) thereof (MH1) (MH2) by said mechanism for adjusting        tip and/or tilt of a surface of a sample (S) placed on a surface        of said stage (STG) for supporting a sample (S).

The sample (S) supporting stage (STG) can be adjusted to be at a desireddistance from a contained magnet (MAG1) (MAG2), by placing at least onelayer of spacer material, (eg. Tape), between the backside of saidsample (S) and said sample supporting stage (STG), and/or by applicationof a motor, (typically a Stepper Motor (SM) or the like), that controls,for instance, relative orientation of the magnetic casing plate (MCP)and interface plate (IP) with respect to one another.

It is convenient to use FIG. 1d to describe the various types ofellipsometers which can be configured from the shown components. Forinstance, a Rotating Polarizer (RP) ellipsometer can be configured bycausing Polarizer Element (WGP1) to rotate during data acquisition. ARotating Analyzer (RA) ellipsometer is configured by causing saidElement (WGP2) to rotate during data acquisition. A Rotating Compensatorellipsometer is configured by making either of the First (RE1) or Second(RE2) shown Rotating Elements be a Compensator and causing it to rotateduring data acquisition. If both (RE1) and (RE2) are made to becompensators and both are caused to rotate during data acquisition, theellipsometer is a Dual Rotating Compensator system. (eg. J.A. WoollamCo. RC2®). This is mentioned as the Cavity (CAV) enhancement of anOutput Signal (OB) can be used in any ellipsometer configuration, evenwhen the system is not applied to investigating the Optical Hall Effect.There are also Modulation element (ME) ellipsometers, in which anelement is made to change some parameter value rather than as caused byrotation of an element. The present invention can be configured as amodulation element system by causing the Cavity (CAV) geometry to bechanged, (ie. modulated), while data is being acquired. This ismentioned as the Cavity (CAV) geometry can be varied very rapidly,thereby leading to a “fast” data acquisition ellipsometer. Again, it isnot necessary that the modulation element system alluded to be appliedonly in practicing Optical Hall Effect investigation. In addition, it ispossible to augment the preferred permanent magnet with an electromagnetand alter the “B” filed applied to a sample by varying currenttherethrough. An electromagnet can be used exclusively, but this isknown in the art.

Turning now to FIGS. 3a and 3b , there is represented in FIG. 3a , athree (3) bounce Odd Bounce image rotating system (OBIRS) comprisingthree (3) reflective elements (REI), (RE2) and (RE3), oriented withrespect to one another such that an input beam of electromagneticradiation (EMI) exits as an output beam of electromagnetic radiation(EMO) without any deviation or displacement being entered into the locusthereof. FIG. 3b demonstrates a five (5) bounce odd bounce imagerotating system (OBIRS) wherein five reflective elements (REI′), (RE2′)(RE3′), (RE4′) and (RE5′) oriented with respect to one another such aninput beam-of electromagnetic radiation (EMI) exits as an output beam ofelectromagnetic radiation (EMO) without any deviation or displacementbeing entered into the locus thereof. Note generally that the angle ofincidence of the (EMI) and (EMO) beams of electromagnetic radiation arenearer normal than is the case in the FIG. 3a three (3) bounce oddbounce image rotating system (OBIRS). This is beneficial in that thecloser to normal the angle of incidence, the less aberration effects areentered to the beam. However, it is also to be appreciated thatconstruction of the FIG. 3b system is more difficult than isconstruction of a FIG. 3a system.

FIGS. 3c-3g show various designs for rotating compensator systems,identifying Reflectors (RM1) (RM2) (RM3) (RM4), and a Total InternalReflection Prism (RP) reflecting surface.

FIGS. 4a and 4b show Mueller Matrix data obtained using the presentinvention which comprises the stage of FIGS. 2a-2e that incorporates apermanent magnet and which is applied at room temperature, and dataobtained from a system which is applied in at much higher B fields,again at room temperature, respectively. To be noted is that the plotsare generally similar, with the difference being that the FIG. 4b datais a better match to a sample model. This shows that the presentinvention, which uses much less costly and more easily accessibleequipment, can be used to provide reasonably good data. FIG. 4c shows ageneral Mueller Matrix configuration, and FIG. 4d shows M12/M11, M21/M11and M33/M11 Mueller Matrix components obtained with no B Field applied.FIG. 4e shows Mueller Matrix Elements M13/M11, M31/M11, M23/M11 andM32/M11 obtained by applying the present invention method with a B fieldapplied, and wherein the data shown is the difference (6) between thatobtained when the Magnet is placed with the North Pole facing onedirection and then the other.

FIG. 5 is included to indicate that it is optimum to provide VIS-MIR andFIR-THz sources that provide output which overlaps in the range of about1.0 to 1.4 THz. FIG. 5 shows that a preferred embodiment of the systemallows sample investigation in both the THz and IR ranges, (eg. from 300GHz to about 1.4 THz, and from about 1.0 THz and higher frequency).Further, it is indicated that below about 1.4 THz a first (31) is usedto provide the electromagnetic radiation, and above about 1.0 THz asecond (S2) Source is used to provide the electromagnetic radiation.FIG. 5 shows an overlap in the range of about 1.0 to about 1.4 THz, andthat a described system preferably provides the same results, (eg.ellipsometic PSI and/or DELTA), when Detector output is analyzed- toprovide, for instance, a Sample characterizing PSI or DELTA. FIG. 5should be viewed as demonstrating a concrete and tangible presentationof results which can be achieved by application of a describedInvention.

FIG. 6 demonstrates displaying data (DIS) provided by a Detector (DET),(DET in FIGS. 1d and 1e ), obtained by practice of described systemsusing machine readable media of a computer (CMP), as well as indicatesthe Computer (CMP) can control Ellipsometer/Polarimeter elementsoperation.

Having hereby disclosed the subject matter of the present invention, itshould be obvious that many modifications, substitutions, and variationsof the present invention are possible in view of the teachings. It istherefore to be understood that the invention may be practiced otherthan as specifically described, and should be limited in scope only bythe Claims.

We claim:
 1. A method of evaluating at least some of free charge carrierlongitudinal and/or transversal effective masses and/or concentrationand/or mobility and/or free charge carrier type in a sample having aback side and a surface, said sample being transparent orsemi-transparent or approaching substantially opaque beyond a distancefrom a surface thereinto at wavelength(s) utilized, said methodcomprising the steps of: a) providing an ellipsometer comprising: asource of a beam of electromagnetic radiation characterized by at leastone wavelength in a selection from the group consisting of the: Visual;MIR; FIR; and THz ranges; a polarizer; a stage for supporting a sample,said stage comprising an adjustable surface that is capable of orientinga sample placed thereupon via adjustment of at least one selection fromthe group consisting of: stage tip, stage tilt and rotation thereofabout an axis projecting substantially normal to said stage surface, todesired value(s); an analyzer; and a detector of relevantelectromagnetic radiation wavelengths; and further providing a source ofa magnetic field; b) placing a sample on said stage and adjusting saidstage so that stage tip and/or stage tilt and/or rotation thereof aboutan axis projecting substantially normal to said stage surface are set todesired values, and so that the source of a magnetic field provides amagnetic field other than parallel thereto at said surface of saidsample; c) while applying the source of a magnetic field to apply aselected magnitude magnetic field other than parallel thereto at thesurface of said sample, causing said source of electromagnetic radiationto provide a beam of electromagnetic radiation of a desired wavelengthwhich is caused to pass through said polarizer and assume a polarizationstate, interact with said sample, pass through said analyzer and entersaid detector which detector produces sample characterizing data; d)from data accumulated by said detector with the system adjusted asdescribed in steps b) and c), evaluating anisotropic values for at leasta partial Jones or Mueller Matrix; and e) from said anisotropic valuesfor said at least a partial Jones or Mueller Matrix determining at leastone of the free charge carrier longitudinal and/or transversal effectivemasses, and/or concentration, and/or mobility and/or type; said methodbeing characterized by at least one selection from the group consistingof: a1′) data is accumulated with the source provided beam ofelectromagnetic radiation set so that it provides at least onesubstantially exact multiple of an optical path length within saidsample; a2′ nine Mueller Matrix are evaluated, said nine elements beingM11, M12, M13, M21, M22, M23, M31, M32 and M33, and wherein each MuellerMatrix elements M12, M13, M21, M22, M23, M31, M32 and M33 is divided bythe value of M11 prior to use in evaluating free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type; a3) at least a partial Mueller matrix is determined and, ofthe Mueller Matrix elements M11, M12, M13, M21, M22, M23, M31, M32 andM33 that can be determined, at least M11, and at least one of M23 andM32 are, said approach to determining values for M11, and at least oneof M23 and M32 being distinguished in that data is determined by aselection from the group consisting of: placing said sample on saidstage for supporting a sample with the back side thereof in contact withsaid stage and obtaining a first set of data, then flipping said sampleso that it's surface is in contact with said stage and obtaining asecond set of data; and first placing the north pole of a permanentmagnet near to the sample and obtaining a first set of data, and thenplacing the south pole of the same or another magnet so that the southpole thereof is near the sample and obtaining a second set of data,followed by subtracting said second set of data from said first, orvice-versa, for each of the resulting M11, and at least one of saidresulting M23 and M32 Mueller Matrix elements determined, and whereineach determined M23 and M32 is divided by M11, prior to using saidresulting at least one of M23 and M32 values as data upon which toregress a model of said sample that includes free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type, thereby allowing their evaluation; a4′) at least one of M13and M3 is determined in addition to M11 by the procedure of obtaining afirst set of data with the sample back side in contact with said stageand then flipping said sample or over so that it's surface is in contactwith said stage and obtaining a second set of data; or by first placingthe north pole of a permanent magnet near to the sample and obtaining afirst set of data, and then placing the south pole of the same oranother magnet so that the it is near the sample and obtaining a secondset of data; and then subtracting said second set of data from saidfirst, or vice-versa, for each of the resulting M11, and at least one ofsaid resulting M13 and M31 Mueller Matrix elements determined, prior tousing said resulting at least one of M23 and M32 and at least one of M13and M31 values as data upon which to simultaneously regress a model ofsaid sample that includes free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type, therebyallowing their evaluation a5′) at least a partial Mueller matrix isdetermined and, of the Mueller Matrix elements M11, M12, M13, M21, M22,M23, M21, M32 and M33 that can be determined, at least M11, and at leastone of M13 and M31 are, said approach to determining values for M11, andat least one of M13 and M31 being distinguished in that data isdetermined by a selection from the group consisting of: placing saidsample on said stage for supporting a sample with the back side thereofin contact with said stage and obtaining a first set of data, thenflipping said sample so that it's surface is in contact with said stageand obtaining a second set of data; and by first placing the north poleof a permanent magnet near to the sample and obtaining a first set ofdata, and then placing the south pole of the same or another permanentmagnet so that is near the sample and obtaining a second set of data;and then subtracting said second set of data from said first, orvice-versa, for each of the resulting M11, and at least one of saidresulting M23 and M32 Mueller Matrix elements determined, and whereineach determined M13 and M31 is divided by M21, prior to using saidresulting at least one of M13 and M31 values as data upon which toregress a model of said sample that includes free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type, thereby allowing their evaluation; a6′) at least one of M32and M23 is determined in addition to M11 by the procedure of data beingdetermined by obtaining a first set of data with the sample back side incontact with said stage and then flipping said sample over so that it'ssurface is in contact with said stage and obtaining a second set ofdata; or by first placing the north pole of a permanent magnet near tothe sample and obtaining a first set of data, and then placing the southpole of the same or another permanent magnet so that is near the sampleand obtaining a second set of data, and then subtracting said second setof data from said first for each of the resulting M11, and at least oneof said resulting M23 and M32 Mueller Matrix elements determined, priorto using said resulting at least one of the M23 and M32 and at least oneof M23 and M32 values as data upon which to simultaneously regress amodel of said sample that includes free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type, therebyallowing their evaluation; and a7′) which Mueller Matrix element M11,and at least one selection from the group of elements consisting of M12,M13, M23, or at least one selection from the group of elementsconsisting of M12, M13, M33 is evaluated by, for each selection, aselection from the group consisting of: first placing said sample onsaid stage for supporting a sample with the back side thereof in contactwith said stage and obtaining a first set of data, and second flippingsaid sample so that it's surface is in contact with said stage andobtaining a second set of data; and by first placing the north pole of apermanent magnet near to the sample and obtaining a first set of data,and second placing the south pole of the same or another magnet so thatit is near the sample and obtaining a second set of data; followed bysubtracting the first from the second or the second from the firstobtained set of data for each selection from the group of elementsconsisting of at least one selection from the group consisting of M12,M13, M23, or at least one selection from the group of elementsconsisting of M12, M13, M33; followed by dividing said result(s) by M11,before, from said anisotropic value(s), determining at least one of thefree charge carrier concentration and/or mobility.
 2. A method as inclaim 1 in which evaluation of said free charge carrier longitudinaland/or transversal effective masses and/or concentration and/or mobilityand/or type is determined based on data acquired when the interaction ofsaid electromagnetic beam of electromagnetic radiation with said sampleinvolves transmission thereof through said sample which is transparentor semi-transparent at wavelength(s) utilized.
 3. A method as in claim 1in which data used in evaluation of said longitudinal and/or transversaleffective masses and/or concentration and/or mobility and/or type isdetermined based on data acquired when the interaction of saidelectromagnetic beam of electromagnetic radiation with said sampleinvolves reflection thereof from said sample which can be substantiallyopaque beyond a distance thereinto from a surface thereof atwavelength(s) utilized.
 4. A method as in claim 1 or 2 or 3 in whichsaid polarizer is set to at least one additional polarization settingand/or wherein said source of a magnetic field set to at least oneadditional magnitude and/or a different wavelength of electromagneticradiation different from that originally utilized is utilized, andadditional data is accumulated by said detector, which additional datais also used in evaluation said free charge carrier longitudinal and/ortransversal effective masses and/or concentration and/or mobility and/ortype.
 5. A method as in claim 1 in which the source of said magneticfield is a permanent magnet that provides a magnetic field of about 1Tor less at the sample surface.
 6. A method as in claim 1 in which thesample is transparent or semi-transparent at wavelength(s) utilized, inwhich said source of said magnetic field is a permanent magnet, andwherein a gap exists between an associated surface thereof from which amagnetic field other than parallel thereto at said sample surfaceemanates, and a backside of said sample.
 7. A method as in claim 1, inwhich the beam of electromagnetic radiation interacts with the sample byreflecting therefrom and in which the stage tip and/or tilt isdetermined based primarily on orienting the surface of said sample sothat the beam of electromagnetic radiation approaches said samplesurface at a desired angle-of-incidence and/or plane-of-incidence.
 8. Amethod as in claim 1, in which the beam of electromagnetic radiationinteracts with the sample by at least partially transmitting through itand in which the stage tip and/or tilt is determined based primarily onsetting a desired gap geometry between a surface associated with saidsource of magnetic field and the backside of said sample, said desiredgap, after being determined being secured in place, followed by saidstage tip and/or tilt being secondarily set to provide anangle-of-incidence and/or plane-of-incidence at which said beam ofelectromagnetic radiation approaches the surface of said sample whilesaid gap geometry is maintained.
 9. A method of determining at leastsome of the free charge carrier concentration and/or mobility in asample, said sample having a back side and a surface and beingtransparent or semi-transparent or substantially opaque beyond somedistance thereinto from a surface thereof thereinto at wavelength(s)utilized, said method comprising the steps of: a) providing anellipsometer comprising: a source of a beam of electromagnetic radiationcharacterized by at least one wavelength in a selection from the groupconsisting of the: Visual; MIR; FIR; and THz ranges; a polarizer; astage for supporting a sample, said stage comprising an adjustablesurface that is capable of orienting a surface of a sample placedthereupon via adjustment of at least one selection from the groupconsisting of: stage tip, stage tilt and rotation thereof about an axisprojecting substantially normal to said stage surface, to desiredvalue(s); an analyzer; and a detector of relevant electromagneticradiation wavelengths; further providing a source of a magnetic field;b) placing a sample on said stage and adjusting said stage so that stagetip and/or stage tilt and/or rotation thereof about an axis projectingsubstantially normal to said stage surface are set to desired values,and so that the source of a magnetic field provides a magnetic fieldother than parallel thereto at said surface of said sample; c) whileapplying the source of a magnetic field to apply a selected magnitudemagnetic field other than parallel thereto at the surface of saidsample, causing said source of electromagnetic radiation to provide abeam of electromagnetic radiation comprising at least one wavelength ofa substantially exact multiple of a an optical path length in saidsample, and which beam is caused to pass through said polarizer andassume a polarization state, interact with said sample, pass throughsaid analyzer and enter said detector, which detector produces samplecharacterizing data; d) from data accumulated by said detector with thesystem adjusted as described in steps b) and c), evaluating anisotropicvalues for at least a partial Jones or Mueller Matrix; and e) from saidanisotropic values for said at least a partial Jones or Mueller Matrixdetermining at least one of the free charge carrier concentration and/ormobility by direct calculation rather than by a mathematical regressionprocedure said method being characterized by at least one selection fromthe group consisting of: a1′) data is accumulated with the sourceprovided beam of electromagnetic radiation set so that it provides atleast one substantially exact multiple of an optical path length withinsaid sample; a2′ nine Mueller Matrix are evaluated, said nine elementsbeing M11, M12, M13, M21, M22, M23, M31, M32 and M33, and wherein eachMueller Matrix elements M12, M13, M21, M22, M23, M31, M32 and M33 isdivided by the value of M11 prior to use in evaluating free chargecarrier longitudinal and transversal effective masses, concentration,mobility and type; a3) at least a partial Mueller matrix is determinedand, of the Mueller Matrix elements M11, M12, M13, M21, M22, M23, M31,M32 and M33 that can be determined, at least M11, and at least one ofM23 and M32 are, said approach to determining values for M11, and atleast one of M23 and M32 being distinguished in that data is determinedby a selection from the group consisting of: placing said sample on saidstage for supporting a sample with the back side thereof in contact withsaid stage and obtaining a first set of data, then flipping said sampleso that it's surface is in contact with said stage and obtaining asecond set of data; and first placing the north pole of a permanentmagnet near to the sample and obtaining a first set of data, and thenplacing the south pole of the same or another magnet so that the southpole thereof is near the sample and obtaining a second set of data,followed by subtracting said second set of data from said first, orvice-versa, for each of the resulting M11, and at least one of saidresulting M23 and M32 Mueller Matrix elements determined, and whereineach determined M23 and M32 is divided by M11, prior to using saidresulting at least one of M23 and M32 values as data upon which toregress a model of said sample that includes free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type, thereby allowing their evaluation; a4′) at least one of M13and M3 is determined in addition to M11 by the procedure of obtaining afirst set of data with the sample back side in contact with said stageand then flipping said sample or over so that it's surface is in contactwith said stage and obtaining a second set of data; or by first placingthe north pole of a permanent magnet near to the sample and obtaining afirst set of data, and then placing the south pole of the same oranother magnet so that the it is near the sample and obtaining a secondset of data; and then subtracting said second set of data from saidfirst, or vice-versa, for each of the resulting M11, and at least one ofsaid resulting M13 and M31 Mueller Matrix elements determined, prior tousing said resulting at least one of M23 and M32 and at least one of M13and M31 values as data upon which to simultaneously regress a model ofsaid sample that includes free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type, therebyallowing their evaluation a5′) at least a partial Mueller matrix isdetermined and, of the Mueller Matrix elements M11, M12, M13, M21, M22,M23, M31, M32 and M33 that can be determined, at least M11, and at leastone of M13 and M31 are, said approach to determining values for M11, andat least one of M13 and M31 being distinguished in that data isdetermined by a selection from the group consisting of: placing saidsample on said stage for supporting a sample with the back side thereofin contact with said stage and obtaining a first set of data, thenflipping said sample so that it's surface is in contact with said stageand obtaining a second set of data; and by first placing the north poleof a permanent magnet near to the sample and obtaining a first set ofdata, and then placing the south pole of the same or another permanentmagnet so that is near the sample and obtaining a second set of data;and then subtracting said second set of data from said first, orvice-versa, for each of the resulting M11, and at least one of saidresulting M23 and M32 Mueller Matrix elements determined, and whereineach determined M13 and M31 is divided by M11, prior to using saidresulting at least one of M13 and M31 values as data upon which toregress a model of said sample that includes free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type, thereby allowing their evaluation; a6′) at least one of M32and M23 is determined in addition to M11 by the procedure of data beingdetermined by obtaining a first set of data with the sample back side incontact with said stage and then flipping said sample over so that it'ssurface is in contact with said stage and obtaining a second set ofdata; or by first placing the north pole of a permanent magnet near tothe sample and obtaining a first set of data, and then placing the southpole of the same or another permanent magnet so that is near the sampleand obtaining a second set of data, and then subtracting said second setof data from said first for each of the resulting M11, and at least oneof said resulting M23 and M32 Mueller Matrix elements determined, priorto using said resulting at least one of the M23 and M32 and at least oneof M23 and M32 values as data upon which to simultaneously regress amodel of said sample that includes free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type, therebyallowing their evaluation; and a7′) which Mueller Matrix element M11,and at least one selection from the group of elements consisting of M12,M13, M23, or at least one selection from the group of elementsconsisting of M12, M13, M33 is evaluated by, for each selection, aselection from the group consisting of: first placing said sample onsaid stage for supporting a sample with the back side thereof in contactwith said stage and obtaining a first set of data, and second flippingsaid sample so that it's surface is in contact with said stage andobtaining a second set of data; and by first placing the north pole of apermanent magnet near to the sample and obtaining a first set of data,and second placing the south pole of the same or another magnet so thatit is near the sample and obtaining a second set of data; followed bysubtracting the first from the second or the second from the firstobtained set of data for each selection from the group of elementsconsisting of at least one selection from the group consisting of M12,M13, M23, or at least one selection from the group of elementsconsisting of M12, M13, M33; followed by dividing said result(s) by M11,before, from said anisotropic value(s), determining at least one of thefree charge carrier concentration and/or mobility.
 10. A method as inclaim 1 or 9 wherein the stage for supporting a sample functionallycomprises: a) an interface plate comprising said sample supportingstage; b) a magnetic casing plate for positioning at least one magnetwith respect to said sample supporting stage; and c) a mechanism foradjusting the tip and/or tilt of said stage with respect to a surfaceassociated with said at least one magnet such that said surfaceassociated with said at least one magnet is substantially parallel tothe back of a sample placed on said sample supporting stage.
 11. Amethod as in claim 10 in which the magnetic casing plate and interfaceplate are offset from one another to provide a gap therebetween, whichgap contributes to formation of a cavity effect wherein at least someelectromagnetic radiation directed at said sample by said source of abeam thereof reflects from said surface associated with said at leastone magnet re-enters said sample.
 12. A method as in claim 10 in whichsaid magnetic casing plate comprises two magnet holders interconnectedby a magnetic material support bar.
 13. A stage for supporting a samplehaving a back side and a surface, comprising: a) an interface platecomprising a sample supporting stage; b) a magnetic casing plate forpositioning at least one magnet with respect to said sample supportingstage, through an opening in said magnetic casing plate said interfaceplate projects; c) a mechanism for adjusting the tip and/or tilt of saidstage with respect to a surface associated with said at least onemagnet, such that said surface associated with said at least one magnetis substantially parallel to the back side of a sample placed on saidsample supporting stage; such that in use said magnetic casing plate andinterface plate are offset from one another and adjusted by saidmechanism for adjusting the tip and/or tilt of said stage to provide agap therebetween that establishes a cavity in which at least someelectromagnetic radiation caused to be incident on the sample surfacetransmits through said sample and reflects from said surface associatedwith said magnet back into said sample, and d) a mechanism for fixingthe described relationship between said magnetic casing plate andinterface plate, and then allowing the tip/tilt mechanism capability beused to adjust an ellipsometer electromagnetic beam angle and/or planeof incidence thereto.
 14. A stage as in claim 13 in which is present atleast one selection from the group consisting of: a) said magneticcasing plate comprises two magnet holders, optionally interconnected bya support bar; b) said gap is set by a mechanism that adjusts therelative orientation between said magnetic casing plate and saidinterface plate; c) said gap is formed by placing spacer materialbetween the back of said sample and a surface of said stage upon whichsaid sample is placed; d) said gap is formed by at a spacer comprisingat least one layer of tape between the back of said sample and a surfaceof said stage upon which said sample is placed; and e) said gap isadjusted by a motor.
 15. A method as in claim 13 in which the samplesupporting stage can be adjusted to be at a desired distance from amagnet, and is so adjusted by placing at least one layer of spacingmaterial between said sample supporting stage and the sample supportedthereby, or by use of a motor.
 16. A method of determining at least oneof free charge carrier concentration and/or mobility in a sample, saidsample having a back side and a surface and being transparent orsemi-transparent at wavelength(s) utilized, said method comprising thesteps of: a) providing an ellipsometer comprising: a source of a beam ofelectromagnetic radiation characterized by at least one wavelengthselected from the group consisting of: Visual; MIR; FIR; and THz ranges;a polarizer; a stage for supporting a sample; an analyzer; and adetector; b) placing a sample on said stage and adjusting said stage sothat stage tip and/or stage tilt and/or rotation thereof about an axisprojecting substantially normal to said stage surface are set to desiredvalues, and so that the source of a magnetic field provides a magneticfield other than parallel thereto at said surface of said sample, and/oradjusting positioning of the source of a magnetic field which isoriented to provide a magnetic field other than parallel thereto at saidsurface of said sample, to achieve a desired value of magnetic field atsaid sample surface; c) while applying the source of a magnetic field toprovide a selected magnitude magnetic field other than parallel theretoat the surface of said sample, causing said source of electromagneticradiation to provide a beam of electromagnetic radiation which is causedto pass through said polarizer and assume a polarization state, interactwith said sample, pass through said analyzer and enter said detector,which detector produces sample characterizing data; d) from dataaccumulated by said detector with the system adjusted as described insteps b) and c), evaluating anisotropic values for at least a partialJones or Mueller Matrix; and e) from said values for said at least apartial Jones or Mueller Matrix determining at least one of the freecharge carrier concentration and/or mobility; said method beingcharacterized by at least one selection from the group consisting of:a1′) data is accumulated with the source provided beam ofelectromagnetic radiation set so that it provides at least onesubstantially exact multiple of an optical path length within saidsample; a2′ nine Mueller Matrix are evaluated, said nine elements beingM11, M12, M13, M21, M22, M23, M31, M32 and M33, and wherein each MuellerMatrix elements M12, M13, M21, M22, M23, M31, M32 and M33 is divided bythe value of M11 prior to use in evaluating free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type; a3) at least a partial Mueller matrix is determined and, ofthe Mueller Matrix elements M11, M12, M13, M21, M22, M23, M31, M32 andM33 that can be determined, at least M11, and at least one of M23 andM32 are, said approach to determining values for M11, and at least oneof M23 and M32 being distinguished in that data is determined by aselection from the group consisting of: placing said sample on saidstage for supporting a sample with the back side thereof in contact withsaid stage and obtaining a first set of data, then flipping said sampleso that it's surface is in contact with said stage and obtaining asecond set of data; and first placing the north pole of a permanentmagnet near to the sample and obtaining a first set of data, and thenplacing the south pole of the same or another magnet so that the southpole thereof is near the sample and obtaining a second set of data,followed by subtracting said second set of data from said first, orvice-versa, for each of the resulting M11, and at least one of saidresulting M23 and M32 Mueller Matrix elements determined, and whereineach determined M23 and M32 is divided by M11, prior to using saidresulting at least one of M23 and M32 values as data upon which toregress a model of said sample that includes free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type, thereby allowing their evaluation; a4′) at least one of M13and M3 is determined in addition to M11 by the procedure of obtaining afirst set of data with the sample back side in contact with said stageand then flipping said sample or over so that it's surface is in contactwith said stage and obtaining a second set of data; or by first placingthe north pole of a permanent magnet near to the sample and obtaining afirst set of data, and then placing the south pole of the same oranother magnet so that the it is near the sample and obtaining a secondset of data; and then subtracting said second set of data from saidfirst, or vice-versa, for each of the resulting M11, and at least one ofsaid resulting M13 and M31 Mueller Matrix elements determined, prior tousing said resulting at least one of M23 and M32 and at least one of M13and M31 values as data upon which to simultaneously regress a model ofsaid sample that includes free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type, therebyallowing their evaluation a5′) at least a partial Mueller matrix isdetermined and, of the Mueller Matrix elements M11, M12, M13, M21, M22,M23, M31, M32 and M33 that can be determined, at least M11, and at leastone of M13 and M31 are, said approach to determining values for M11, andat least one of M13 and M31 being distinguished in that data isdetermined by a selection from the group consisting of: placing saidsample on said stage for supporting a sample with the back side thereofin contact with said stage and obtaining a first set of data, thenflipping said sample so that it's surface is in contact with said stageand obtaining a second set of data; and by first placing the north poleof a permanent magnet near to the sample and obtaining a first set ofdata, and then placing the south pole of the same or another permanentmagnet so that is near the sample and obtaining a second set of data;and then subtracting said second set of data from said first, orvice-versa, for each of the resulting M11, and at least one of saidresulting M23 and M32 Mueller Matrix elements determined, and whereineach determined M13 and M31 is divided by M11, prior to using saidresulting at least one of M13 and M31 values as data upon which toregress a model of said sample that includes free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type, thereby allowing their evaluation; a6′) at least one of M32and M23 is determined in addition to M11 by the procedure of data beingdetermined by obtaining a first set of data with the sample back side incontact with said stage and then flipping said sample over so that it'ssurface is in contact with said stage and obtaining a second set ofdata; or by first placing the north pole of a permanent magnet near tothe sample and obtaining a first set of data, and then placing the southpole of the same or another permanent magnet so that is near the sampleand obtaining a second set of data, and then subtracting said second setof data from said first for each of the resulting M21, and at least oneof said resulting M23 and M32 Mueller Matrix elements determined, priorto using said resulting at least one of the M23 and M32 and at least oneof M23 and M32 values as data upon which to simultaneously regress amodel of said sample that includes free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type, therebyallowing their evaluation; and a7′) which Mueller Matrix element M11,and at least one selection from the group of elements consisting of M12,M13, M23, or at least one selection from the group of elementsconsisting of M12, M13, M33 is evaluated by, for each selection, aselection from the group consisting of: first placing said sample onsaid stage for supporting a sample with the back side thereof in contactwith said stage and obtaining a first set of data, and second flippingsaid sample so that it's surface is in contact with said stage andobtaining a second set of data; and by first placing the north pole of apermanent magnet near to the sample and obtaining a first set of data,and second placing the south pole of the same or another magnet so thatit is near the sample and obtaining a second set of data; followed bysubtracting the first from the second or the second from the firstobtained set of data for each selection from the group of elementsconsisting of at least one selection from the group consisting of M12,M13, M23, or at least one selection from the group of elementsconsisting of M12, M13, M33; followed by dividing said result(s) by M11,before, from said anisotropic value(s), determining at least one of thefree charge carrier concentration and/or mobility.
 17. A method as inclaim 1 or 9 or 16 in which the data is acquired at room temperature.18. A method as in claim 1 or 9 or 16 in which the ellipsometer furthercomprises at least one compensator between the source of a beam ofelectromagnetic radiation and the detector.
 19. A method as in claim 1or 9 or 16 in which the permanent magnet utilized provides a fieldstrength at the sample of between about 0.6 and 1.5 Tesla.
 20. A methodof enhancing the capability of determining at least one of free chargecarrier concentration and/or mobility in a sample having a back side anda surface, said sample being transparent or semi-transparent atwavelength(s) utilized, said method comprising the steps of: a)providing an ellipsometer comprising: a source of a beam ofelectromagnetic radiation characterized by at least one wavelength in aselection from the group consisting of the: Visual; MIR; FIR; and THz;ranges; a polarizer; a stage for supporting a sample; an analyzer; and adetector; and a source of a magnetic field having a surface associatedtherewith and which is oriented to provide a magnetic field other thanparallel thereto at said surface of said sample; b) placing a sample onsaid stage and adjusting said stage so that stage tip and/or stage tiltand/or rotation thereof about an axis projecting substantially normal tosaid stage surface are set to desired values, and so that the source ofa magnetic field provides a magnetic field other than parallel theretoat said surface of said sample, and/or further adjusting the source of amagnetic field so that it is oriented to provide a magnetic field otherthan parallel thereto at said surface of said sample of a desired value;c) while applying the source of a magnetic field to apply a magneticfield other than parallel thereto at the surface of said sample or adesired value, causing said source of electromagnetic radiation toprovide a beam of electromagnetic radiation comprising at least onewavelength which is substantially a multiple of an optical path lengthin said sample, which beam is caused to pass through said polarizer andassume a polarization state, interact with said sample, pass throughsaid analyzer and enter said detector, which detector produces samplecharacterizing data; d) from data accumulated by said detector with thesystem adjusted as described in steps b) and c), evaluating anisotropicvalues for at least a partial Jones or Mueller Matrix; and e) from saidvalues for said at least a partial Jones or Mueller Matrix directlydetermining at least one of the free charge carrier concentration and/ormobility; said method being distinguished in that, while data is beingaccumulated by said detector, a gap is caused to exist between at leastone selection from the group consisting of: 1) said sample backside andthe sample supporting stage; and 2) said sample supporting stage andsaid surface associated with said source of a magnetic field which isoriented to provide a magnetic field other than parallel thereto at saidsurface of said sample of a desired value; such that a cavity is formedin which at least some electromagnetic radiation in the beam thereofdirected at said sample by said source of a beam of electromagneticradiation passes through said sample, and is coherently reflected backthereinto by said surface associated with said source of a magneticfield, thereby enhancing the signal entering the detector; said methodbeing characterized by at least one selection from the group consistingof: a1′) data is accumulated with the source provided beam ofelectromagnetic radiation set so that it provides at least onesubstantially exact multiple of an optical path length within saidsample; a2′ nine Mueller Matrix are evaluated, said nine elements beingM11, M12, M13, M21, M22, M23, M31, M32 and M33, and wherein each MuellerMatrix elements M12, M13, M21, M22, M23, M31, M32 and M33 is divided bythe value of M11 prior to use in evaluating free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type; a3) at least a partial Mueller matrix is determined and, ofthe Mueller Matrix elements M11, M12, M13, M21, M22, M23, M31, M32 andM33 that can be determined, at least M11, and at least one of M23 andM32 are, said approach to determining values for M11, and at least oneof M23 and M32 being distinguished in that data is determined by aselection from the group consisting of: placing said sample on saidstage for supporting a sample with the back side thereof in contact withsaid stage and obtaining a first set of data, then flipping said sampleso that it's surface is in contact with said stage and obtaining asecond set of data; and first placing the north pole of a permanentmagnet near to the sample and obtaining a first set of data, and thenplacing the south pole of the same or another magnet so that the southpole thereof is near the sample and obtaining a second set of data,followed by subtracting said second set of data from said first, orvice-versa, for each of the resulting M11, and at least one of saidresulting M23 and M32 Mueller Matrix elements determined, and whereineach determined M23 and M32 is divided by M11, prior to using saidresulting at least one of M23 and M32 values as data upon which toregress a model of said sample that includes free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type, thereby allowing their evaluation; a4′) at least one of M13and M3 is determined in addition to M11 by the procedure of obtaining afirst set of data with the sample back side in contact with said stageand then flipping said sample or over so that it's surface is in contactwith said stage and obtaining a second set of data; or by first placingthe north pole of a permanent magnet near to the sample and obtaining afirst set of data, and then placing the south pole of the same oranother magnet so that the it is near the sample and obtaining a secondset of data; and then subtracting said second set of data from saidfirst, or vice-versa, for each of the resulting M11, and at least one ofsaid resulting M13 and M31 Mueller Matrix elements determined, prior tousing said resulting at least one of M23 and M32 and at least one of M13and M31 values as data upon which to simultaneously regress a model ofsaid sample that includes free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type, therebyallowing their evaluation a5′) at least a partial Mueller matrix isdetermined and, of the Mueller Matrix elements M11, M12, M13, M21, M22,M23, M31, M32 and M33 that can be determined, at least M11, and at leastone of M13 and M31 are, said approach to determining values for M11, andat least one of M13 and M31 being distinguished in that data isdetermined by a selection from the group consisting of: placing saidsample on said stage for supporting a sample with the back side thereofin contact with said stage and obtaining a first set of data, thenflipping said sample so that it's surface is in contact with said stageand obtaining a second set of data; and by first placing the north poleof a permanent magnet near to the sample and obtaining a first set ofdata, and then placing the south pole of the same or another permanentmagnet so that is near the sample and obtaining a second set of data;and then subtracting said second set of data from said first, orvice-versa, for each of the resulting M11, and at least one of saidresulting M23 and M32 Mueller Matrix elements determined, and whereineach determined M13 and M31 is divided by M11, prior to using saidresulting at least one of M13 and M31 values as data upon which toregress a model of said sample that includes free charge carrierlongitudinal and transversal effective masses, concentration, mobilityand type, thereby allowing their evaluation; a6′) at least one of M32and M23 is determined in addition to M11 by the procedure of data beingdetermined by obtaining a first set of data with the sample back side incontact with said stage and then flipping said sample over so that it'ssurface is in contact with said stage and obtaining a second set ofdata; or by first placing the north pole of a permanent magnet near tothe sample and obtaining a first set of data, and then placing the southpole of the same or another permanent magnet so that is near the sampleand obtaining a second set of data, and then subtracting said second setof data from said first for each of the resulting M11, and at least oneof said resulting M23 and M32 Mueller Matrix elements determined, priorto using said resulting at least one of the M23 and M32 and at least oneof M23 and M32 values as data upon which to simultaneously regress amodel of said sample that includes free charge carrier longitudinal andtransversal effective masses, concentration, mobility and type, therebyallowing their evaluation; and a7′) which Mueller Matrix element M11,and at least one selection from the group of elements consisting of M12,M13, M23, or at least one selection from the group of elementsconsisting of M12, M13, M33 is evaluated by, for each selection, aselection from the group consisting of: first placing said sample onsaid stage for supporting a sample with the back side thereof in contactwith said stage and obtaining a first set of data, and second flippingsaid sample so that it's surface is in contact with said stage andobtaining a second set of data; and by first placing the north pole of apermanent magnet near to the sample and obtaining a first set of data,and second placing the south pole of the same or another magnet so thatit is near the sample and obtaining a second set of data; followed bysubtracting the first from the second or the second from the firstobtained set of data for each selection from the group of elementsconsisting of at least one selection from the group consisting of M12,M13, M23, or at least one selection from the group of elementsconsisting of M12, M13, M33; followed by dividing said result(s) by M11,before, from said anisotropic value(s), determining at least one of thefree charge carrier concentration and/or mobility.
 21. A method as inclaim 20, in which the gap is caused to exist by placing spacer materialbetween said sample back side and said sample supporting stage.
 22. Amethod as in claim 20, in which the gap is caused to exist byapplication of a motor applied between an interface plate that comprisessaid sample supporting stage and a magnet casing plate that comprisessaid surface associated with said source of a magnetic field which isoriented to provide a magnetic field other than parallel thereto at saidsurface of said sample.
 23. A method as in claim 1 or 9 or 16 or 20 inwhich the polarizer is a rotatable polarizer and the analyzer is arotating analyzer.
 24. A method as in claim 1 or 9 or 16 or 20 in whichthe magnetic field which is applied other than parallel thereto at thesurface of said sample is applied substantially, or exactlyperpendicular to said sample surface.
 25. A method as in claim 1 or 9 or16 or 20 which further comprises a compensator between said source anddetector.
 26. A method as in claim 1 or 16 or 20 which appliesmathematical regression to Jones or Mueller matrix elements to arrive atthe desired values.
 27. A method as in claim 1 or 16 or 20 which appliesdirect mathematical calculation to Jones or Mueller matrix elements toarrive at the desired values for concentration and/or mobility of chargecarriers present.
 28. A method as in claim 1 or 9 or 16 or 20 in whichthe said source of a magnetic field is at least one permanent magnet,and in which the sample is transparent or semitransparent and the is agap present under said sample, which gap contributes to formation of acavity effect wherein at least some electromagnetic radiation directedat said sample by said source of a beam thereof reflects from saidsurface associated with said at least one magnet re-enters said sample,the effect thereof being to enhance the signal entering said detector.29. A method as in claim 11 or 13 or 20 in which the said cavitygeometry is modulated in size during data acquisition.
 30. Anellipsometer system comprising: a polarization state generator; a stagefor supporting a sample, said stage having a substantially flat surface;and a polarization state detector; such that in use said polarizationstate generator directs a polarized beam of electromagnetic radiation tointeract with a sample on said stage for supporting a sample, whichafter said interaction presents as a beam of electromagnetic radiationthat enters said polarization state detector, that in response producessample characterizing data; said ellipsometer system being distinguishedin that said stage for supporting a sample is functionally a part of aresonate cavity that directs electromagnetic radiation that passesthrough a transparent or semi-transparent sample supported upon saidstage having a substantially flat surface to be reflected back into saidtransparent or semi-transparent sample, such that when samplecharacterizing data is being accumulated by said polarization statedetector, it is enhanced over what it would be otherwise as a result ofcoherent interaction in said transparent or semi-transparent samplebetween electromagnetic radiation incident thereupon provided by saidpolarization state generator, and electromagnetic radiation thatreflects back into said transparent or semi-transparent sample as aresult of said resonance effect, a resulting coherent combination ofsaid two identified contributions of electromagnetic radiation in saidsample then comprising said beam that enters said polarization statedetector; said system being characterized by the presence of a magnetcasing plate, such that in use a magnet is secured thereto in a mannersuch that a magnetic field directed other than parallel thereto at thesample surface is presented to said sample.
 31. A system as in claim 30in which said system further comprises a mechanism that enables aligningthe substantially flat surface of said stage and the substantially flatsurface associated with said magnet so that they are substantiallyparallel to one another by a tip/tilt procedure.
 32. A system as inclaim 31 in which it is said stage for supporting a sample that iscaused to undergo said tip/tilt procedure to align the substantiallyflat surface associated with said magnet substantially parallel to thestage substantially flat surface.
 33. A system as in claim 31 in whichit is said substantially flat surface associated with said magnet thatis caused to undergo said tip/tilt procedure to align the substantiallyflat surface associated with said magnet substantially parallel to thestage substantially flat surface.
 34. A system as in claim 31 in whichsaid substantially flat surface associated with said magnet is caused bealigned substantially parallel to the stage substantially flat surfaceand then said resulting orientation is secured in place, followed bysaid tip/tilt procedure being practiced primarily to align said stagesubstantially flat surface so that desired angle-of-incidence and/orplane-of-incidence of said beam of electromagnetic radiation caused tobe directed at said sample by said polarization state generator, is/areachieved.
 35. A system as in claim 30 or 31 or 32 or 33 or 34 in whichthe resonance effect is enhanced by placing spacer material between thestage for supporting a sample and a sample supported thereby, or byapplication of a motor.
 36. A method of evaluating at least some of freecharge carrier longitudinal and/or transversal effective masses and/orconcentration and/or mobility and/or free charge carrier type in asample having a back side and a surface, said sample being transparentor semi-transparent or approaching substantially opaque beyond adistance from a surface thereinto at wavelength(s) utilized, said methodcomprising the steps of: a) providing an ellipsometer comprising: asource of a beam of electromagnetic radiation characterized by at leastone wavelength in a selection from the group consisting of the: Visual;MIR; FIR; and THz ranges, a polarizer; a stage for supporting a sample,said stage comprising an adjustable surface that is capable of orientinga sample placed thereupon via adjustment of at least one selection fromthe group consisting of: stage tip, stage tilt and rotation thereofabout an axis projecting substantially normal to said stage surface, todesired value(s); an analyzer; and a detector of relevantelectromagnetic radiation wavelengths; and further providing a source ofa magnetic field; b) placing a sample on said stage and adjusting saidstage so that stage tip and/or stage tilt and/or rotation thereof aboutan axis projecting substantially normal to said stage surface are set todesired values, and so that the source of a magnetic field provides amagnetic field other than parallel thereto at said surface of saidsample; c) while applying the source of a magnetic field to apply aselected magnitude magnetic field other than parallel thereto at thesurface of said sample, causing said source of electromagnetic radiationto provide a beam of electromagnetic radiation of a desired wavelengthwhich is caused to pass through said polarizer and assume a polarizationstate, interact with said sample, pass through said analyzer and entersaid detector which detector produces sample characterizing data; d)from data accumulated by said detector with the system adjusted asdescribed in steps b) and c), evaluating anisotropic values for at leasta partial Jones or Mueller Matrix; and e) from said anisotropic valuesfor said at least a partial Jones or Mueller Matrix determining at leastone of the free charge carrier longitudinal and/or transversal effectivemasses, and/or concentration, and/or mobility and/or type.
 37. A methodof determining at least some of free charge carrier concentration and/ormobility in a sample, said sample having a back side and a surface andbeing transparent or semi-transparent or substantially opaque beyondsome distance thereinto from a surface thereof thereinto atwavelength(s) utilized, said method comprising the steps of: a)providing an ellipsometer comprising: a source of a beam ofelectromagnetic radiation characterized by at least one wavelength in aselection from the group consisting of the: Visual; MIR; FIR; and THzranges; a polarizer; a stage for supporting a sample, said stagecomprising an adjustable surface that is capable of orienting a surfaceof a sample placed thereupon via adjustment of at least one selectionfrom the group consisting of: stage tip, stage tilt and rotation thereofabout an axis projecting substantially normal to said stage surface, todesired value(s); an analyzer; and a detector of relevantelectromagnetic radiation wavelengths; further providing a source of amagnetic field; b) placing a sample on said stage and adjusting saidstage so that stage tip and/or stage tilt and/or rotation thereof aboutan axis projecting substantially normal to said stage surface are set todesired values, and so that the source of a magnetic field provides amagnetic field other than parallel thereto at said surface of saidsample; c) while applying the source of a magnetic field to apply aselected magnitude magnetic field other than parallel thereto at thesurface of said sample, causing said source of electromagnetic radiationto provide a beam of electromagnetic radiation comprising at least onewavelength of a substantially exact multiple of a an optical path lengthin said sample, and which beam is caused to pass through said polarizerand assume a polarization state, interact with said sample, pass throughsaid analyzer and enter said detector, which detector produces samplecharacterizing data; d) from data accumulated by said detector with thesystem adjusted as described in steps b) and c), evaluating anisotropicvalues for at least a partial Jones or Mueller Matrix; and e) from saidanisotropic values for said at least a partial Jones or Mueller Matrixdetermining at least one of the free charge carrier concentration and/ormobility by direct calculation rather than by a mathematical regressionprocedure.
 38. A method of determining at least one of free chargecarrier concentration and/or mobility in a sample, said sample having aback side and a surface and being transparent or semi-transparent atwavelength(s) utilized, said method comprising the steps of: a)providing an ellipsometer comprising: a source of a beam ofelectromagnetic radiation characterized by at least one wavelengthselected from the group consisting of: Visual; MIR; FIR; and THz ranges;a polarizer; a stage for supporting a sample; an analyzer; and adetector; b) placing a sample on said stage and adjusting said stage sothat stage tip and/or stage tilt and/or rotation thereof about an axisprojecting substantially normal to said stage surface are set to desiredvalues, and so that the source of a magnetic field provides a magneticfield other than parallel thereto at said surface of said sample, and/oradjusting positioning of the source of a magnetic field which isoriented to provide a magnetic field other than parallel thereto at saidsurface of said sample, to achieve a desired value of magnetic field atsaid sample surface; c) while applying the source of a magnetic field toprovide a selected magnitude magnetic field other than parallel theretoat the surface of said sample, causing said source of electromagneticradiation to provide a beam of electromagnetic radiation which is causedto pass through said polarizer and assume a polarization state, interactwith said sample, pass through said analyzer and enter said detector,which detector produces sample characterizing data; d) from dataaccumulated by said detector with the system adjusted as described insteps b) and c), evaluating anisotropic values for at least a partialJones or Mueller Matrix; and e) from said values for said at least apartial Jones or Mueller Matrix determining at least one of the freecharge carrier concentration and/or mobility.
 39. A method of enhancingthe capability of determining at least one of free charge carrierconcentration and/or mobility in a sample having a back side and asurface, said sample being transparent or semi-transparent atwavelength(s) utilized, said method comprising the steps of: a)providing an ellipsometer comprising: a source of a beam ofelectromagnetic radiation characterized by at least one wavelength in aselection from the group consisting of the: Visual; MIR; FIR; and THz;ranges; a polarizer; a stage for supporting a sample; an analyzer; and adetector; and a source of a magnetic field having a surface associatedtherewith and which is oriented to provide a magnetic field other thanparallel thereto at said surface of said sample; b) placing a sample onsaid stage and adjusting said stage so that stage tip and/or stage tiltand/or rotation thereof about an axis projecting substantially normal tosaid stage surface are set to desired values, and so that the source ofa magnetic field provides a magnetic field other than parallel theretoat said surface of said sample, and/or further adjusting the source of amagnetic field so that it is oriented to provide a magnetic field otherthan parallel thereto at said surface of said sample of a desired value;c) while applying the source of a magnetic field to apply a magneticfield other than parallel thereto at the surface of said sample or adesired value, causing said source of electromagnetic radiation toprovide a beam of electromagnetic radiation comprising at least onewavelength which is substantially a multiple of an optical path lengthin said sample, which beam is caused to pass through said polarizer andassume a polarization state, interact with said sample, pass throughsaid analyzer and enter said detector, which detector produces samplecharacterizing data; d) from data accumulated by said detector with thesystem adjusted as described in steps b) and c), evaluating anisotropicvalues for at least a partial Jones or Mueller Matrix; and e) from saidvalues for said at least a partial Jones or Mueller Matrix directlydetermining at least one of the free charge carrier concentration and/ormobility; said method being distinguished in that, while data is beingaccumulated by said detector, a gap is caused to exist between at leastone selection from the group consisting of: 1) said sample backside andthe sample supporting stage; and 2) said sample supporting stage andsaid surface associated with said source of a magnetic field which isoriented to provide a magnetic field other than parallel thereto at saidsurface of said sample of a desired value; such that a cavity is formedin which at least some electromagnetic radiation in the beam thereofdirected at said sample by said source of a beam of electromagneticradiation passes through said sample, and is coherently reflected backthereinto by said surface associated with said source of a magneticfield, thereby enhancing the signal entering the detector.